He was ruled out for Sunday's game at the Los Angeles Lakers and will be re-evaluated this week to determine when he can return to play.
Westbrook suffered the injury with 2.5 seconds remaining in the fourth quarter against the Portland Trail Blazers on Friday when teammate Andre Roberson inadvertently kneed him in the face, leaving a visible dent in the side of his face.
Westbrook left the game without speaking to reporters in order to carry out further evaluation at a local medical facility.
The zygomatic arch bone separates the eye socket from the sinuses.
Westbrook had his third consecutive triple-double against the Blazers, scoring 40 points with 13 rebounds and 11 assists. He had a historic February, averaging 31.2 points, 9.1 rebounds and 10.3 assists, numbers that only ever have been totaled by Hall of Famer Oscar Robertson.
Kevin Durant is set to be re-evaluated for a minor procedure he underwent last Sunday and could return as soon as this week. In seven games without Durant in February, Westbrook averaged a triple-double -- 31.2 points, 10.0 rebounds and 11.3 assists.
Westbrook, 26, is averaging 26.5 points, 6.8 rebounds and 8.1 assists in 45 games this season. He missed 14 games in November because of a fracture in his right hand.
Newly acquired D.J. Augustin will start in place of Westbrook on Sunday against the Lakers.