But not in the way you might think.
According to Islam, Jesus was a holy prophet of Allah, just like Moses and the other biblical prophets. "Jesus was a Muslim."
However, Muslims do not recognize the divinity of Jesus. They do not believe that:
he was the son of God
he was born from a virgin
he performed miracles
he resurrected after his death
he is part of the holy Trinity
Why not? Because Muhammad, the greatest and final prophet of Islam, said so. He received a dream in a cave 600 years after Jesus' death, telling him that Jesus' story was incorrect and that Jesus was simply a prophet.
Remember, the story of Jesus had been originally told to us by witnesses who lived during his life, heard his words coming from his mouth and saw his death and resurrection first-hand. And it wasn't just some random witnesses, it was the Apostles, his most devoted followers. Aside from Judas (who committed suicide) and John (who died of old age), all 10 other Apostles died as martyrs to spread Jesus' - and thus God's - message.
So we now have a situation in which Muslims believe in Jesus, yet they do not believe in any of the core beliefs of Christianity. There are only 3 possible ways to explain this inconsistency:
1. Jesus lied
2. The Apostles lied
3. Muhammad lied
If Jesus was a liar, this means that one of Islam's holy prophets was a liar. Logically, a religion with a false prophet can only be a FALSE religion.
If the Apostles were liars, this means that a holy prophet of Allah could attract nothing but liars to tell Allah's message, making Jesus a false prophet. Logically, a religion with a false prophet can only be a FALSE religion.
If Muhammad was a liar, this means that the ultimate and most important prophet of Islam was a liar. Logically, a religion with a false prophet can only be a FALSE religion.
There is no escape to be found in either reason or faith: no matter how you look at it, Islam is mathematically and undeniably a FALSE religion.