Thompson left Wednesday night’s game against the Indiana Pacers in the second quarter and didn’t return.
He exited the arena on crutches with his left leg in a brace and underwent an MRI on Thursday.
Jae Crowder will replace Thompson in the starting lineup.
Thompson, 26, is averaging 4.4 points and 6.4 rebounds in eight games this season.
The Cavaliers’ 124-107 loss to the Pacers on Wednesday was their fourth straight defeat.
ESPN’s Dave McMenamin contributed to this report.