Yes they do. But there are some differences to the way Christians believe in him.
Muslims don't believe that Jesus (May Peace Be Upon Him) was God or the Son of God.
What Muslims Believe about him.
- He was born of the Virgin Mary (May Allah be pleased with her).
- He and his mother were both humans, nothing else.
- He was a prophet of God like the many other prophets of God sent before him like Moses, Abraham, David, Solomon, Noah etc.
- He preached the worshipping of one almighty God only.
- All the miracles associated with him were performed by the permission and will of God.
- He is the second most highly revered prophet in Islam.
- He was not crucified on the cross. A man of similar liking was replaced with him and he is in heaven right now.
- He will return very soon. It will be just before sunrise, somewhere in the present day Syria region.
- Upon his return he shall lead an army and kill the antichrist.
- After the death of the antichrist, there will be 40 years of peace.
- He will get married and live until his natural death.
- Muslims cannot be Muslims if they don’t believe in the above information about him.
These are only a handful of beliefs about Jesus in Islam. An additional 5 dozen pointers could have been mentioned for a much thorough but longer answer.