As others have said, "The Prophet" is Jesus.
The prophet being Jesus is better than Mohammed because Moses' prophecy (Deuteronomy 18:15) says that he will arise "from your midst, of your brethren." The NET renders the idiom "your brethren" this way:
18:15 The Lord your God will raise up for you a prophet like me from among you – from your fellow Israelites; you must listen to him.
Their translation is spot on.
As Moses addressed this to the Hebrews, the Prophet will arise from the Hebrews. I have known Muslims who say that the phrase "from your brethren" refers to coming from the children of Ishmael, the brother of Isaac. However, brother in this time meant "fellow member of the covenant community."
In the Old Testament, this phrase referred to those related by blood. As time progressed, this changed. The term "brethren" referred to more than just blood but those who share beliefs. Tobit (3rd century BC), Jubilees (3rd to 2nd century BC), and Ben Sirach (late third to early second century BC) all refer to people who do not share a blood line but share a bond in the covenant as "brothers." This nuance was noted by R.H. Charles in The Apocrypha and Pseudepigrapha of the Old Testament (Oxford: Clarendon, 1931, 1:321 note 3 to Ben Sira 10:20).
This interpretation became so prevalent that it was even read back into texts with religious significance. Philo (On the Virtues 82) explains, "Moses means by the term 'brother' not only one who is born of the same parents as oneself, but everyone who is a fellow citizen or fellow countryman."
Moreover, looking at the phrase in the rest of Deuteronomy, shows that "brethren" does often mean "fellow Israelite." For example:
Deuteronomy 15:2 This is the nature of the cancellation: Every creditor must remit what he has loaned to another person; he must not force payment from his fellow Israelite, for it is to be recognized as “the Lord’s cancellation of debts.”
Deuteronomy 15:3 You may exact payment from a foreigner, but whatever your fellow Israelite owes you, you must remit.
Deuteronomy 15:7 If a fellow Israelite from one of your villages in the land that the Lord your God is giving you should be poor, you must not harden your heart or be insensitive to his impoverished condition.
Deuteronomy 23:19 You must not charge interest on a loan to your fellow Israelite, whether on money, food, or anything else that has been loaned with interest.
This is so from the very beginning of the book:
Deuteronomy 1:16 I furthermore admonished your judges at that time that they should pay attention to issues among your fellow citizens and judge fairly, whether between one citizen and another or a citizen and a resident foreigner.
In that use, Moses points out that a foreigner cannot be a "brother." (Once proselytism became practiced, it was possible for a foreigner to be a brother, however, he was no longer considered a foreigner.
In the nail in the coffin response to the children-of-Ishmael-are-brothers-to-the-children-of-Isaac argument, please see Deuteronomy 17:15:
Deuteronomy 17:15 you must select without fail a king whom the Lord your God chooses. From among your fellow citizens you must appoint a king – you may not designate a foreigner who is not one of your fellow Israelites.
This is the same phrase as used in chapter 18 and it points out that the king must be a native born Israelite. The king could not be a foreigner of any kind. Likewise, the prophet would have to be a native born Israelite.