Short answer
Yes. The Qur'an calls Muhammad (ﷺ) "the Seal of the Prophets". A seal was the stamp pressed on a letter once it was finished. It closes the letter, and nothing is added after it. The Prophet (ﷺ) said it in plain words too: there will be no prophet after me. He compared himself to the last brick that completes a house. Muslims see three more reasons. The religion was declared complete during his farewell pilgrimage, a few months before he died. The prophets before him were sent to their own peoples, but he was sent to all people. And many earlier prophets came to restore messages that had been lost or changed. The Qur'an has been kept whole, so nothing is left to restore. This is why Muslims hold that Muhammad (ﷺ) is the last prophet.
Full explanation
The Seal of the Prophets
The Qur'an names Muhammad (ﷺ) khatam al-nabiyyin, the Seal of the Prophets. In the Arabic of his day, a khatam (seal) was the stamp a writer pressed on a letter once he had finished it. Muslim scholars read the word as the one who closes the line of prophets. After him, no prophet is added.
“Muhammad is not the father of any of your men, but (he is) the Messenger of Allah, and the Seal of the Prophets: and Allah has full knowledge of all things.”
In the Prophet's (ﷺ) own words
The Prophet (ﷺ) described all the prophets as one house with a single brick missing. He called himself that brick. He also said that among the Israelites one prophet followed another, but that after him there would be no prophet. And he said that no prophet came between Jesus and himself.
Abu Hurayra reports that the Prophet (ﷺ) compared himself and the prophets before him to a man who built a fine house but left the place of one brick empty in a corner. People walked round it, admired it, and wished the brick were in place. He said: I am that brick, and I am the last of the prophets.
Abu Hurayra reports that the Prophet (ﷺ) said the Israelites were led by prophets, and whenever one died another took his place. But there will be no prophet after me, he said; there will be caliphs, and many of them.
Abu Hurayra reports that the Prophet (ﷺ) said he was the nearest of all people to the son of Mary. The prophets are brothers with one father, he said, and there was no prophet between him and Jesus.
A religion declared complete
The Qur'an records the moment the religion was finished. The verse came down on a Friday at Arafat, a plain outside Mecca, during the farewell pilgrimage of the Prophet (ﷺ). This was a few months before he died. Umar ibn al-Khattab, one of the Prophet's (ﷺ) leading Companions (the followers who knew him), confirmed the day and the place. A complete religion needs no further prophet. Another one would mean that God (﷾) had left something out.
“This day have I perfected your religion for you, completed My favour upon you, and have chosen for you Islam as your religion.”
A Jewish man told Umar ibn al-Khattab that if the verse "This day have I perfected your religion" had been revealed to the Jews, they would have kept that day as a festival. Umar answered that Muslims know exactly when and where it came down: on a Friday, while the Prophet (ﷺ) was standing at Arafat during the pilgrimage.
Sent to all people, not to one nation
While Jesus was teaching, he said he was sent only to the lost sheep of the house of Israel. He told his disciples not to go to the Gentiles (the non-Jews). The Prophet (ﷺ) was told to say that he was sent to all mankind. He also said that every prophet before him was sent to his own people only. A prophet for one nation is naturally followed by a prophet for the next. A message for everyone has no successor to wait for.
“But he answered and said, I am not sent but unto the lost sheep of the house of Israel.”
“These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: But go rather to the lost sheep of the house of Israel.”
“Say: "O men! I am sent unto you all, as the Messenger of Allah, to Whom belongeth the dominion of the heavens and the earth: there is no god but He: it is He That giveth both life and death. So believe in Allah and His Messenger, the Unlettered Prophet, who believeth in Allah and His words: follow him that (so) ye may be guided."”
“We sent thee not, but as a Mercy for all creatures.”
Jabir ibn Abdullah reports that the Prophet (ﷺ) named five things given to him that no prophet before him was given. The last of them: every earlier prophet was sent to his own nation only, but he was sent to all mankind.
Why prophets kept coming, and why they stopped
The Qur'an says a messenger was sent to every people. It says many more were sent than it names. Some prophets came to peoples who had never had one. Others came to call a people back to a message they had lost or changed, or to lead them by it. The Qur'an ends that need. God (﷾) promised to guard it. The Companions memorised it in the lifetime of the Prophet (ﷺ). It was written down under his direction. It was gathered soon after his death. It was sent to all people. So there is no people left without the message, and no lost message left to restore.
“For We assuredly sent amongst every People a messenger, (with the Command), "Serve Allah, and eschew Evil": of the People were some whom Allah guided, and some on whom error became inevitably (established). So travel through the earth, and see what was the end of those who denied (the Truth).”
“We did aforetime send messengers before thee: of them there are some whose story We have related to thee, and some whose story We have not related to thee. It was not (possible) for any messenger to bring a sign except by the leave of Allah: but when the Command of Allah issued, the matter was decided in truth and justice, and there perished, there and then those who stood on Falsehoods.”
“We have, without doubt, sent down the Message; and We will assuredly guard it (from corruption).”
“Say: "O men! I am sent unto you all, as the Messenger of Allah, to Whom belongeth the dominion of the heavens and the earth: there is no god but He: it is He That giveth both life and death. So believe in Allah and His Messenger, the Unlettered Prophet, who believeth in Allah and His words: follow him that (so) ye may be guided."”
Zayd ibn Thabit reports that after many who knew the Qur'an by heart were killed at Yamama, Abu Bakr asked him to gather the Qur'an into one volume, reminding him that he used to write down the revelation for the Messenger of Allah. Zayd collected it from written pieces and from the memories of men, and the finished copy passed from Abu Bakr to Umar and then to Hafsa.
What finality does not mean
It does not mean the Prophet (ﷺ) was set above the other prophets in a way that divides them. Muslims make no distinction between God's (﷾) messengers in believing in them. It does not mean God (﷾) has stopped listening. He answers everyone who calls on Him. Nor does it rule out Jesus' return. The Prophet (ﷺ) said the son of Mary will descend while the Muslims' own leader (the imam) is among them. Muslims hold that Jesus returns as a follower of the Qur'an, bringing no new book. The Prophet (ﷺ) said that when the Muslims' leader invites him to lead the prayer, he will decline. In the report about the son of Mary descending among them, the narrator Ibn Abi Dhi'b gives the meaning. Jesus will lead them by the Book of their Lord and the Sunnah (the way) of their Prophet (ﷺ). Finality means that no new prophet will be sent, because the message is complete and kept. Jesus was a prophet before Muhammad (ﷺ), so his return adds none.
“The Messenger believeth in what hath been revealed to him from his Lord, as do the men of faith. Each one (of them) believeth in Allah, His angels, His books, and His messengers. "We make no distinction (they say) between one and another of His messengers." And they say: "We hear, and we obey: (We seek) Thy forgiveness, our Lord, and to Thee is the end of all journeys."”
“When My servants ask thee concerning Me, I am indeed close (to them): I listen to the prayer of every suppliant when he calleth on Me: Let them also, with a will, Listen to My call, and believe in Me: That they may walk in the right way.”
Abu Hurayra reports that the Prophet (ﷺ) asked his companions how they would be when the son of Mary descends among them while their own imam is among them.
Jabir reports that the Prophet (ﷺ) said Jesus son of Mary will descend, and the Muslims' leader will invite him to lead the prayer. Jesus will decline and say that the Muslims' leaders are from among themselves, an honour from Allah to this community.
In 155a Abu Huraira reports that the Prophet (ﷺ) swore the son of Mary will soon descend as a just judge, break the cross, kill the swine and end the jizya. In 155f the Prophet asks how it will be when the son of Mary descends and leads the Muslims as one of them; the narrator Ibn Abi Dhi'b explains that he will lead them by the Book of their Lord and the Sunnah of their Prophet.
Abu Hurayra reports that the Prophet (ﷺ) said the Israelites were led by prophets, and whenever one died another took his place. But there will be no prophet after me, he said; there will be caliphs, and many of them.
Why he is the last prophet: the key points
- The Qur'an calls Muhammad (ﷺ) the Seal of the Prophets. A seal (khatam) was the stamp pressed on a letter once it was finished.
- He said there would be no prophet after him, and called himself the last brick that completes a house.
- The religion was declared complete on a Friday at Arafat, during his farewell pilgrimage.
- Earlier prophets were sent to their own peoples. He was sent to all people.
- Many earlier prophets came to restore a message that had been lost or changed. God (﷾) promised to guard the Qur'an, so nothing is left to restore.
- It does not set him above the other prophets in a way that divides them, and God (﷾) still answers everyone who calls on Him. Jesus will return, but as a follower of the Qur'an, with no new book.
The Christian view
Christians hold that God's (﷾) last word came in Jesus. They point to the opening of the Letter to the Hebrews, a book of the New Testament. It says God (﷾) spoke through the prophets, and in these last days through his Son.
“God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets, Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;”
Verse by verse
Hebrews 1:1-2 — Epistle to the Hebrews, chapter 1, verses 1-2
“God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets, Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;”
Cited for
God's speaking through the Son in "these last days" is final, so no prophet can come after Jesus.
The response
Hebrews is a letter by an unnamed writer, not a saying of Jesus. Jesus himself said he had many things still to tell his disciples that they could not bear yet. He said the Spirit of truth would come to guide them into all truth. Muslims hold that this promised one is the Prophet (ﷺ). The Paraclete page explains why. Jesus also told the chief priests and elders that the kingdom of God (﷾) would be taken from them and given to another nation.
Where it lands — By Jesus' own words his teaching was not the last word, and the Gospels leave room for the one who came after him.
Perspectives
Sikh: the Gurus came after
Sikhs honour ten Gurus, from Guru Nanak in the fifteenth century to Guru Gobind Singh, and the Guru Granth Sahib after them. Guru Arjan writes that the Guru and the Transcendent Lord, the Lord beyond all things, are one.
Guru Arjan writes that the Guru and the Transcendent Lord are One (Ang 864). So guidance came again after Muhammad (ﷺ).
Rebuttal
The Qur'an calls Muhammad (ﷺ) the Seal of the Prophets, and he said there would be no prophet after him. A later teacher may say true things. But the test of any claim to speak for God (﷾) is whether it matches the message He has guarded. And if "the Guru" means a man, the Qur'an's messenger says he himself is only a man like those who hear him.
Ahmadi: the seal means the best, not the last
The Ahmadiyya community holds that khatam in Qur'an 33:40 means a seal of excellence: the best and most perfect. So, they say, a prophet can still come who brings no new law and follows Muhammad (ﷺ).
Khatam means a seal or "the best and most perfect". In the Prophet's (ﷺ) time, they say, it was never used to mean "last".
Rebuttal
The dictionaries do give "last". Lane and Ibn Manzur list it and name this verse, and the community's own article also grants "the last of the Prophets" as a meaning. The Prophet (ﷺ) settled it himself: the Israelites were led by prophets, one after another, but there will be no prophet after me.
Mainstream Christian
God's final word was spoken through Jesus, the Son. No prophet after Jesus' first disciples brings a new revelation.
Hebrews says that God, who once spoke through the prophets, has in these last days spoken through his Son.
Rebuttal
Hebrews is a letter by an unnamed writer, not a saying of Jesus. Jesus himself said he had more to tell his disciples than they could bear. He said the Spirit of truth would come to guide them into all truth. So by his own words, his teaching was not the last word.
The Islamic perspective
Muhammad (ﷺ) is the last prophet. The Qur'an says so, and he said so. The religion was declared complete, his message is for everyone, and the book he brought has not been lost.
The Qur'an calls Muhammad (ﷺ) the Seal of the Prophets.
The Prophet (ﷺ) said there would be no prophet after him. He compared himself to the last brick that completes a house.
The Qur'an declared the religion perfected at Arafat, during the farewell pilgrimage.
Earlier prophets were sent to their own peoples, while Muhammad (ﷺ) was sent to all mankind.
Prophets were sent to new peoples, or to bring back messages that were lost or changed. A message for everyone, which God (﷾) has guarded, needs neither.
Jesus himself said he had more to teach than his disciples could bear. He said the Spirit of truth would come and guide them into all truth.