The Grizzlies updated Miller's status on Thursday.
Miller scored 11 points Wednesday night as the Grizzlies won their fourth straight in Sacramento. But he hurt his thumb late and immediately signaled to the Grizzlies' bench for help before heading directly to the locker room.
The veteran signed with Memphis last summer and has played all 44 games with the Grizzlies this season averaging 21.5 minutes per game.
The Grizzlies visit Minnesota on Friday night.