The injury occurred in the second quarter of his side's defeat to the Los Angeles Clippers when he was clipped by the elbow of teammate Kendrick Perkins while going up for a rebound.
The Thunder are now without two key players following an injury to reigning league MVP Kevin Durant, who is not expected to return until later this month.
General manager Sam Presti told ESPN: "The circumstances that we're being presented with right now are temporary. It's our job to eliminate the dramatics and harness our mentality and make sure that we're productively using the time.
"When those guys do come back and we start to get our full complement of players, we have built a collective mentality and momentum that's only going to be accelerated when we get our group together."
The Thunder are now 0-2 in their season following their defeat to the Clippers.