Short answer
No. Muslims believe Jesus, like all the prophets, was protected by Allah from sin. The Quran calls him "a pure boy", and authentic hadith say Satan did not touch him at birth and that on the Day of Judgement he will not mention any sin of his. This does not make him divine: Muslims believe every prophet was protected by Allah.
Sunni creed holds that prophets are protected ('isma) from kufr and from major and minor sins. Al-Fiqh al-Akbar adds that some prophets had slips (zallat), which are not sins of disobedience. No slip of Jesus is mentioned in the Quran or authentic hadith.
The four schools agree on this.
Explanation
When the angel came to Mary, he said he brought news of "a pure boy". The Quran adds that Jesus would be "of the righteous". The Prophet ﷺ said every child of Adam is touched by Satan at birth and cries out from it, except Mary and her son.
A striking detail comes in the long hadith of intercession. On the Day of Judgement people go from prophet to prophet asking for help. Adam, Noah, Abraham and Moses each mention a slip that makes them hesitate. When they reach Jesus he declines too, but the narrator notes that he did not mention any sin, and sends them to Muhammad ﷺ.
In Islam, though, being free of sin is not proof of divinity. All prophets are protected (ma'sum) so that people can follow them safely. Muslims say the same of Muhammad ﷺ; see did Prophet Muhammad ever sin? The Quran praises Yahya (John the Baptist) as honourable and righteous too. Jesus ate, slept, prayed and worshipped Allah, all marks of a human servant.
So Muslims and Christians agree that Jesus was without sin, but for different reasons. For Christians it is tied to his being God the Son. For Muslims it is Allah's gift to a chosen messenger. See is Jesus God in Islam?
The evidence
Quran, Surah Maryam 19:19
قَالَ إِنَّمَآ أَنَا۠ رَسُولُ رَبِّكِ لِأَهَبَ لَكِ غُلَٰمًۭا زَكِيًّۭا ﴿١٩﴾
He said, "I am only the messenger of your Lord to give you [news of] a pure boy."
The angel described Jesus as pure.
Quran, Surah Aal-i-Imraan 3:46
وَيُكَلِّمُ ٱلنَّاسَ فِى ٱلْمَهْدِ وَكَهْلًۭا وَمِنَ ٱلصَّٰلِحِينَ ﴿٤٦﴾
He will speak to the people in the cradle and in maturity and will be of the righteous."
Jesus is among the righteous.
Quran, Surah Aal-i-Imraan 3:39
فَنَادَتْهُ ٱلْمَلَٰٓئِكَةُ وَهُوَ قَآئِمٌۭ يُصَلِّى فِى ٱلْمِحْرَابِ أَنَّ ٱللَّهَ يُبَشِّرُكَ بِيَحْيَىٰ مُصَدِّقًۢا بِكَلِمَةٍۢ مِّنَ ٱللَّهِ وَسَيِّدًۭا وَحَصُورًۭا وَنَبِيًّۭا مِّنَ ٱلصَّٰلِحِينَ ﴿٣٩﴾
So the angels called him while he was standing in prayer in the chamber, "Indeed, Allah gives you good tidings of John, confirming a word from Allah and [who will be] honorable, abstaining [from women], and a prophet from among the righteous."
Other prophets, like John, are also praised for purity, so it is not a sign of divinity.
Sahih al-Bukhari 3431
Sahih... يمسه الشيطان حين يولد فيستهل صارخا من مس الشيطان غير مريم وابنها ...
"Every child of Adam is touched by Satan when born and cries out from his touch, except Mary and her son."
Jesus was protected from Satan from his birth.
Sahih al-Bukhari 4712
Sahih... ولن يغضب بعده مثله ولم يذكر ذنبا نفسي نفسي ...
"Jesus will say his Lord is angry as never before or after, and he will not mention any sin, then say: myself, myself."
Unlike the other prophets in the hadith, Jesus mentions no sin.
Where the ruling is recorded
- al-Fiqh al-Akbar, the section on the prophets. States that the prophets are free of minor and major sins, while some had slips.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.