An MRI showed that Smart suffered a left ankle sprain and bone bruising during Friday's win over the Indiana Pacers.
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.
The Celtics (2-3) play at Chicago on Saturday.