How do Christians explain Muhammad being mentioned in the Gospel of Barnabas?

Nigel’s answer is absolutely correct!

But besides the solid answer he gives, we have other evidence that this is not part of the Canon and should be solidly rejected. Revelation is not only the last book in the collection of the New Testament but its also the last book chronologically-thus making the bookend. In Revelation, John said that nothing else can be added- No new Revelation- the Canon is closed.

The Canon was determined by the Holy spirit- not a church council, or a priest bowling league.

Furthermore- because scripture is inspired by God, there are no contradictions- only apparent ones, which are usually issues of translations, and or Gentiles not understanding Jewish worldview, culture and idioms.

Historical Facts:

The last book of the Bible was written before the end of the first century. Muhammad died in 632 (the seventh century) but the Qur’an and Hadiths were not written till later.

The Gospel of Barnabas was not written until at least the fifteenth century.

The author of the Gospel of Barnabas could not have been the biblical Barnabas.

Here is a partial quote from an article that explains the origins of the Gospel of Barnabas:

The real Barnabas was a generous encourager of the early church (Acts 4:36-37). He was not one of the original twelve disciples of Jesus as the Gospel of Barnabas mistakenly claims. Barnabas was the one who persuaded the apostles that Paul had changed from a persecutor of the church to a follower of Jesus (Acts 9:27). The true Barnabas was a missionary, telling the good news of Jesus (Acts 13:2).

If the Gospel of Barnabas were written in the first century, it would have been quoted in other documents of the same time period. It is not cited, however, a single time in works of either the church fathers or Muslim clerics until the fifteenth century. The Gospel of Barnabas contains quotations from Dante Alighieri, references to an edict from Pope Boniface, and descriptions of feudalism. Therefore, scholars place the date of authorship around the fifteenth century. Source: https://www.gotquestions.org/Muslim-Barnabas.html

Conclusion: The Gospel of Barnabas was written some fifteen hundred years after the life, death and resurrection of Jesus. Since it was also written after the life and death of Muhammad, then that explains why it mentions Muhammad – it was written after the event.

Christians do not have to explain anything. The onus on proving anything in the Gospel of Barnabas is divinely inspired by God or speaks the truth falls to Muslims, not Christians.

The content of the so-called "Gospel of Barnabas" is so wildly contradictory to all the other books of the New Testament scriptures that it is thoroughly rejected from the canon of scripture.

It is supposed to originate in the 16th or 17th centuries and appears to borrow from Dante (1265-1321).

This work clearly contradicts the New Testament biblical accounts of Jesus and his ministry but has strong parallels with the Islamic faith, not only mentioning Muhammad by name, but including the shahadah (chapter 39). It is strongly anti-Pauline and anti-Trinitarian in tone. In this work, Jesus is described as a prophet and not the son of God,[47] while Paul is called "the deceived."[48] Furthermore, the Gospel of Barnabas states that Jesus escaped crucifixion by being raised alive to heaven, while Judas Iscariot the traitor was crucified in his place. These beliefs—in particular, that Jesus is a prophet of God and raised alive without being crucified—conform to or resemble Islamic teachings which say that Jesus is a major prophet who did not die on the cross but was taken alive by angels to God..

This work should not be confused with the surviving Epistle of Barnabas, nor with the surviving Acts of Barnabas.

Wikipedia - Gospel of Barnabas

There is no compelling reason whatsoever for Christians to give credence to this blatant falsification.