He suffered the injury during Saturday's game against the New Orleans Pelicans.
Baker, the Knicks' second-year guard, tried to prevent the Pelicans' Anthony Davis from dunking in the second quarter of New York's win. Davis' forearm slammed against Baker's face on the play, leading to the fracture.
Davis completed the dunk, and Baker was whistled for a foul on the play. Baker immediately left the game after the play because of a cut on his face.
The Knicks say Baker is day-to-day.