Black can do it in three moves:
Quickest Knight checkmate
Here's one in three:
1. e3 Nc6 2. c3 Ne5 3. Ne2 Nd3#
Ok, so I cheated a little. The rules didn't say who was to mate. I think it's impossible for white to mate with a knight in less than four moves. Black needs to move two pawns and block the king/queen/bishop with a knight. That makes three black moves so white can't mate before move four.
edit: I see OBIT beat me to it. :)
I don't actually know if anyone has posted the solution for the quickest knight check mate, but I have a checkmate in 4 moves. If anyone found a quicker one, I'd love someone to show it to me.
This challenge was from a posting from IM David Pruess on Chess.com TV