God repeats some of what He had said in verse 15, but the difference is instructive! Verse 15 says, ". . . a Prophet like me," while verse 18 says, ". . . a Prophet like you"! In verse 15, God says the Prophet will be like Himself, but in verse 18, He says He will be like "you."
To whom does the pronoun "you" refer: to the Israelites generally, or to Moses specifically? Is this prophet to be merely human, like the Israelites, or would he be human with special attributes, more like Moses? This prophet, though human, will be somewhat like God, who promises to put His words in this Prophet's mind and mouth. The prophet will then repeat every word God commands to his brethren.
Can this scripture apply to Moses himself? Yes, but it applies to Moses only insofar as any human being—even one filled with and guided by God's Holy Spirit—can be like God. (In this way this could also apply to others like Samuel, Elijah, Jeremiah, Daniel, John the Baptist, and the apostle Paul.) A primary function of this Prophet is to act as a mediator between God and His people. Comparing these verses to Deuteronomy 5:5, we can see that Moses was the first human mediator between God and His people and thus fulfilled this prophecy, at least in type: "I stood between the LORD and you at that time, to declare to you the word of the LORD."
Can this prophecy refer to Jesus Christ, the Son of God, through prophetic duality? Yes, it most definitely can! In fact, some Bible scholars maintain that Jesus, during His human sojourn, is the primary fulfillment of these verses. On the first day of the New Testament church of God, Peter quotes part of Deuteronomy 18, and applies it to Jesus (Acts 3:19-20, 22-23).
Just weeks before, on the last night of His human life, Jesus had told His disciples that He is the Mediator, the One to whom the Father gave a message to pass on to those who would listen and obey (John 14:10, 24).