Smart, who will reportedly undergo an MRI later Friday, was taken off the court on a stretcher.
Celtics coach Brad Stevens commented on Smart's injury after the game. "We're gonna take him in for a look. It's sprained or broken, we don't know. We're hoping it's a sprain," he said.
The Celtics selected Smart with the No. 6 pick in this year's draft out of Oklahoma State.
The 6-foot-4, 220-pound point guard has averaged 7.8 points, 1.5 assists and 1.5 rebounds over four games this season. He left Friday's game after scoring three points in 16 minutes.