The 6-foot-11 Kanter is averaging 14 points and 7.9 rebounds. He was acquired along with Steve Novak from the Utah Jazz in a trade at the deadline last week.
Thunder coach Scott Brooks said it not certain how long Kanter will be out. Brooks believed the injury occurred in the second half of Thursday night's 117-113 overtime loss in Phoenix.
The Thunder have been stung this season by injuries. Kevin Durant missed his fifth straight game Friday night because of ongoing issues with his right foot, and center Steven Adams' right hand fracture has kept him out of eight games.