Short answer. No — quite the opposite. Jesus is one of the greatest prophets in Islam, and Mary is the most honored woman in the Quran. Muslims simply do not believe Jesus was God or the son of God.
Where the idea comes from
Because Islam does not accept the divinity of Jesus or the doctrine of the Trinity, people often assume it must reject or disrespect him. In fact a Muslim cannot even be a Muslim without believing in Jesus as a prophet of God.
Jesus in Islam: prophet and Messiah
The Quran calls Jesus the Messiah and honors him as a word and a sign from God:
"[And mention] when the angels said, 'O Mary, indeed Allah gives you good tidings of a word from Him, whose name will be the Messiah, Jesus, the son of Mary — distinguished in this world and the Hereafter and among those brought near [to Allah].'"
— Quran 3:45 (Saheeh International)1
Muslims affirm his virgin birth and the miracles he performed by God's permission — healing the blind, curing the sick, and giving life to the dead.478 Where Islam parts from Christianity is on his nature: Jesus is revered as a great messenger, not as divine.
"...So believe in Allah and His messengers. And do not say, 'Three'; desist — it is better for you. Indeed, Allah is but one God..."
— Quran 4:171 (Saheeh International)5
The Prophet Muhammad ﷺ underlined this closeness between the prophets:
"Both in this world and in the Hereafter, I am the nearest of all the people to Jesus, the son of Mary. The prophets are paternal brothers; their mothers are different, but their religion is one."
— Sahih al-Bukhari 34436
Mary: the most honored woman in the Quran
Mary — Maryam in Arabic — is the only woman mentioned by name in the Quran, and an entire chapter (the 19th) bears her name. She is held up as chosen and pure above all women:798
"And [mention] when the angels said, 'O Mary, indeed Allah has chosen you and purified you and chosen you above the women of the worlds.'"
— Quran 3:42 (Saheeh International)2
The Quran tells her story with deep tenderness — the angel's visit, her trial, and God's care for her in childbirth (Quran 19:16-21).3
For the fuller picture, see Jesus in Islam and Mary in Islam, and how they fit among the prophets and the revealed books.
In short
Islam does not reject Jesus and Mary — it venerates them. Jesus is a beloved prophet and the Messiah, born of the Virgin Mary, who is herself the most honored woman in the Quran. The difference with Christianity is about who Jesus was — a messenger of God rather than God — not about whether he deserves honor.