Brown suffered the injury during Wednesday's 116-103 loss to the Detroit Pistons, a contest in which he put up 24 points and 12 rebounds in 37 minutes.
"I sprained my right thumb," Brown said after Wednesday's game, per NESN's Lauren Campbell. "Working with the staff to figure out a plan for [Thursday]. ... Happened in the middle of the game. Ran into Markieff."
He added, though, that he didn't consider the injury to be "too bad."
In his fourth NBA season, Brown appears to be taking the leap many expected from him last year. He is averaging 20.0 points, 6.9 rebounds and 2.3 assists while shooting 49.2 percent from the field.
Brown previously missed a total of four games earlier this season due to illness.