1. A Prophet like Moses.
There were hardly any two prophets who were so much alike as Moses and Muhammad. Both were given a comprehensive law and code of life. Both encountered their enemies and were victorious in miraculous ways. Both were accepted as prophets and statesmen. Both migrated following conspiracies to kill them. Analogies between Moses and Jesus overlook not only the above similarities but other crucial ones as well. These include the natural birth, the family life, and the death of Moses and Muhammad but not that of Jesus. Moreover, Jesus was regarded by his followers as the Son of God and not exclusively as a prophet, as Moses and Muhammad were and as Muslims believe Jesus was. So, this prophecy refers to Muhammad and not to Jesus, because Muhammad was more like Moses than Jesus.
Also, one notices that from the Gospel of John that the Jews were waiting for the fufillment of three distinct prophecies: 1) the coming of Christ. 2)The coming of Elijah. 3) The coming of the Prophet. This is obvious from the three questions that were posed to John the Baptist: "Now this was John's testimony, when the Jews of Jerusalem sent priests and Levites to ask him who he was. He did not fail to confess, but confessed freely, 'I am not the Christ.' They asked him, 'Then who are you? Are you Elijah?' He said, "I am not.' 'Are you the Prophet?' He answered, 'No.'" [John 1:19-21] My Study Bible has cross references, and the marginal notes in it link Deut. 18:18 to the question of Are You The Prophet? that the Jews asked John the Baptist. I conclude that Jesus Christ is not the prophet in Deut. 18:18
2. From the Brothers of the Israelites
Abraham had two sons, Issac and Ishmael. Ishmael became the grandfather of the Arab race and Issac became the grandfather of the Jewish nation. The prophet spoken of was not to come from among the Jews themselves, but from among their brothers, i.e. the Ishmaelites. Muhammad, a descendant of Ishmael, is indeed this prophet. Also, Isaiah 42:1-13 speaks of the servant of God, His 'chosen one and messenger' who will bring down a law. "He will not falter or be discouraged till he establishes Justice on earth. In his law the islands will put their hope." Verse 11 connects that awaited messenger with the descendants of Kedar. Who is Kedar? Kedar was the second son of Ishmael, and ancestor to the Prophet Muhammad.
3. God will put His words in the mouth of this Prophet. The Words of God were truly put into Muhammad's mouth. God sent the Angel Gabriel to teach Muhammad the exact words of God and asked him to dictate them to the people as he heard them. The words are therefore not his own. They did not come from his own thoughts but were put into his mouth by Gabriel.
Note that God said in the prophecy of Deutronomy: "If anyone does not listen to my words that the prophet speaks in my name, I myself will call him to account." [Deut. 18:19] This means whoever believes in the Bible must believe in what this prophet says, and this prophet is Muhammad.
I rest my case.