The prophet in Deuteronomy 18:18 is non other than Prophet Muhammad (saw).
The whole of Deut 18:18 - 22 is talking about one special prophet that will be raised up.
In Deuteronomy 34:10 "Arise not a prophet ever again in Israel like Moses...". However the translation in all Bible translation was unscrupulous. The only prophet known who is not from Israel but a brother to the Israelites or a close of kin is Prophet Muhammad (saw).
Deuteronomy 18:22 does not talk about a false prophet but about the prophet that God raised up. This verse is another false translation by most bible translators, who translate "Hannavi" as "a prophet" to show that it can be any false prophet. "Hannavi" means "The Prophet".
Jesus cannot be that prophet as Jesus himself rose up from Israel. If the Christians insist that it was Jesus, than Jesus must be the prophet that spoke in defiance to God and deserves the death penalty. Christians believe that Jesus died a horrible death.
Some Jews believe that the prophet could be Joshua the Nun, however Deut 34:10 does not allow this in its context.
Links:
http://www.blueletterbible.org/