Short answer
No. Neither Jesus nor his apostles were white Europeans. The Gospels never describe his face, his height, his hair or his colouring. No portrait of him survives from his lifetime. He was a Jew of Roman Palestine who spoke Aramaic. He was circumcised, he kept the Sabbath, and he never set foot in Europe. His apostles were Galileans like him, and a Roman officer once took the apostle Paul for an Egyptian. The Jesus on church walls is not a portrait. His long hair, beard and robes took shape in Roman and Byzantine (eastern Roman) art from the fourth century. European painters later made him fair and blue-eyed, with their own faces. In one report in al-Bukhari, the Prophet Muhammad (ﷺ) describes him, seen in a dream, as a man of brown complexion with straight hair. No report speaks of blond hair or blue eyes.
Full explanation
What the Gospels say about his looks
Nothing. No Gospel gives his height, his colouring, his hair or his face, and no image of him survives from his lifetime or anywhere near it. Many of the earliest Christian pictures, from the third century, show a young man without a beard. The long-haired, bearded, robed figure became the standard type in Roman and Byzantine art from the fourth century onwards, and later European painting fixed it. Historians who have studied the question conclude that he looked like other Judaean men of his time.
A historian of early Judaism and Christianity at King's College London. She notes that the Gospels never describe Jesus' appearance, traces the familiar long-haired, bearded, robed figure to later Christian art, above all Byzantine images of Christ enthroned, and argues that he most likely looked like other Judaean men of his day: dark hair, brown eyes and olive to brown skin.
A Jew of Roman Palestine
Mark keeps some of his words in Aramaic, the language of Galilee. They include the words he spoke to raise a girl and, in Mark's telling, his cry on the cross. Luke records that he was circumcised on the eighth day and that he went to the synagogue on the Sabbath, as his custom was. His life was lived between Galilee and Jerusalem.
“And he took the damsel by the hand, and said unto her, Talitha cumi; which is, being interpreted, Damsel, I say unto thee, arise.”
“And at the ninth hour Jesus cried with a loud voice, saying, Eloi, Eloi, lama sabachthani? which is, being interpreted, My God, my God, why hast thou forsaken me?”
“And when eight days were accomplished for the circumcising of the child, his name was called JESUS, which was so named of the angel before he was conceived in the womb.”
“And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read.”
The apostles came from the same land
The apostles were men of the same land and people. Peter and his brother Andrew were fishermen on the Sea of Galilee. In Jerusalem, Peter's way of speaking gave him away as a Galilean. At Pentecost, the Jewish feast fifty days after Passover, the crowd said of the apostles: "are not all these which speak Galileans?" Paul, who also called himself an apostle, was a Jew of Tarsus, in what is now Turkey. A Roman officer who arrested him in Jerusalem asked him, "Art not thou that Egyptian", taking him for a known Egyptian rebel. No one in the New Testament describes any of them as fair-skinned or European. Like Jesus, they were men of the Middle East.
“And Jesus, walking by the sea of Galilee, saw two brethren, Simon called Peter, and Andrew his brother, casting a net into the sea: for they were fishers.”
“And he denied it again. And a little after, they that stood by said again to Peter, Surely thou art one of them: for thou art a Galilean, and thy speech agreeth thereto.”
“And they were all amazed and marvelled, saying one to another, Behold, are not all these which speak Galileans?”
“And as Paul was to be led into the castle, he said unto the chief captain, May I speak unto thee? Who said, Canst thou speak Greek? Art not thou that Egyptian, which before these days madest an uproar, and leddest out into the wilderness four thousand men that were murderers? But Paul said, I am a man which am a Jew of Tarsus, a city in Cilicia, a citizen of no mean city: and, I beseech thee, suffer me to speak unto the people.”
How the Prophet (ﷺ) described him
A hadith is a report of what the Prophet (ﷺ) said. In one report, al-Bukhari 3441, the Prophet (ﷺ) described Jesus as shown to him in a dream at the Ka'ba. He saw a man of brown complexion with straight hair, water dripping from his head. Ibn Umar, a companion of the Prophet (ﷺ) in the seventh century, reported it. Nothing in the hadith describes a blond, blue-eyed European.
Ibn Umar reports that the Prophet (ﷺ) described a dream in which, while going round the Ka'ba, he saw a man of brown complexion (adam in Arabic) with straight hair, water dripping from his head, and was told that this was the son of Mary.
Sent to Israel, not to Europe
Jesus said he was sent only to the lost sheep of the house of Israel. He told his disciples not to go to the Gentiles, who are non-Jews. During his ministry he sent his disciples only to Israel. The command to go to all nations comes only in accounts that Christians say tell of Jesus after the resurrection. Years later, the book of Acts tells of the early Church. In it, the Jewish believers were astonished that the Holy Spirit had come on the Gentiles too. The religion preached in his name later became the religion of Europe. The Qur'an says the Prophet (ﷺ) was sent to all mankind.
“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.”
“And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.”
“We have not sent thee but as a universal (Messenger) to men, giving them glad tidings, and warning them (against sin), but most men understand not.”
The figure people see in visions
Many Christians report seeing Jesus in a dream or vision. The figure they describe is usually the robed man familiar from church paintings. The Gospels give no description, so there is nothing to check such a figure against. It matches later art, not the man who walked in Galilee. Paul, a Christian missionary of the first century, warned that Satan can appear as an angel of light. So a shining figure in a vision is no proof by itself. The Law, the Torah, says a dreamer is judged by his message, not by his sign. And if Jesus did appear, that would show only that he is alive, which Muslims believe. It would not show that he is God, or that he died for anyone, as Christians believe. Islam has a further check. The Prophet's (ﷺ) appearance was recorded in detail, and he said that Satan cannot take his form. Ibn Sirin was a Muslim scholar of dreams in the generation after the companions. He added that this holds only when he is seen as he really was. And by the Law's own test, a figure who says 'I am God' fails, however brightly it shines.
“And no marvel; for Satan himself is transformed into an angel of light.”
“If there arise among you a prophet, or a dreamer of dreams, and giveth thee a sign or a wonder, And the sign or the wonder come to pass, whereof he spake unto thee, saying, Let us go after other gods, which thou hast not known, and let us serve them; Thou shalt not hearken unto the words of that prophet, or that dreamer of dreams: for the Lord your God proveth you, to know whether ye love the Lord your God with all your heart and with all your soul.”
“Nay, Allah raised him up unto Himself; and Allah is Exalted in Power, Wise;-”
A historian of early Judaism and Christianity at King's College London. She notes that the Gospels never describe Jesus' appearance, traces the familiar long-haired, bearded, robed figure to later Christian art, above all Byzantine images of Christ enthroned, and argues that he most likely looked like other Judaean men of his day: dark hair, brown eyes and olive to brown skin.
Anas reports that the Prophet (ﷺ) said: whoever sees me in a dream has truly seen me, because Satan cannot take my form.
Abu Hurayra reports that the Prophet (ﷺ) said Satan cannot take his form in a dream. Al-Bukhari adds that Muhammad ibn Sirin, one of the Successors, said this holds only when the Prophet is seen in his real form.
Perspectives
What historians conclude
Jesus was a Galilean Jew of the first century. Nothing written in his time describes his looks, and the familiar image comes from later art.
No Gospel describes his appearance, and no portrait of him survives from his lifetime.
The long-haired, bearded, robed figure took shape in Christian art from the fourth century onwards.
He most likely looked like other Judaean men of his day. He would have had dark brown to black hair, brown eyes and olive-brown skin.
Mark preserves words he spoke in Aramaic.
He was circumcised on the eighth day and kept the Sabbath in the synagogue.
His apostles were Galileans, and a Roman officer took the apostle Paul, a Jew of Tarsus, for an Egyptian.
The Islamic perspective
Jesus was a prophet of the Children of Israel, a man of the Middle East. In one report the Prophet (ﷺ) described him as he was shown to him, and no report speaks of blond hair or blue eyes.
In one report in al-Bukhari the Prophet (ﷺ) describes Jesus as a man of brown complexion with straight hair. No report describes blond hair or blue eyes.
Jesus said he was sent only to the lost sheep of the house of Israel.
The Qur'an teaches that the Prophet Muhammad (ﷺ) was sent to all mankind.
Paul warned that Satan can appear as an angel of light, so a vision alone proves nothing.
The Law judges a dreamer by his message. Even a real vision of Jesus would show only that he is alive, which Muslims believe.