Deuteronomy 18:15-19 (NASB)
The LORD your God will raise up for you a prophet like me from among you, from your countrymen, you shall listen to him. This is according to all that you asked of the LORD your God in Horeb on the day of the assembly, saying, "Let me not hear again the voice of the LORD my God, let me not see this great fire anymore, or I will die." The LORD said to me, "They have spoken well. I will raise up a prophet from among their countrymen like you, and I will put My words in his mouth, and he shall speak to them all that I command him. It shall come about that whoever will not listen to My words which he shall speak in My name, I Myself will require it of him."
In Deuteronomy 18, Moses is speaking to the nation of Israel and informing them that one of their brethren or countrymen from among them, thus a fellow Israelite, thus a descendant of Jacob (Genesis 32:28), will be raised up as a prophet of God.
Since Muhammad was not an Israelite, not a descendant of Jacob, this cannot be referring to him.
Additionally (and more importantly), since Muhammad was not a prophet of God, this cannot be referring to him.
Finally, in Acts 3, the apostle Peter, filled with the Holy Spirit, makes it perfectly clear that this prophecy of a coming prophet like Moses was fulfilled in Jesus Christ, who was not only a prophet of God, but was also an Israelite and a descendant of Jacob (Luke 3:23-38; Matthew 1:1-16).
Since this prophecy is explicitly fulfilled in Jesus, it seems unlikely that it is referring to another person as well.
In sum, it is not referring to Muhammad because:
1. Muhammad was not an Israelite.
2. Muhammad was not a prophet.
3. Muhammad was not Jesus.