The All-Star forward was averaging 13.6 points and 6.1 rebounds in 23 games this season.
Baker suffered the injury during the second quarter of Friday's loss at Golden State and is expected to miss four to six weeks.
Baker isn't sure how the injury happened, saying that the basketball may have jammed his thumb or he may have caught it in another player's jersey.
He reentered the game in the third quarter with his thumb heavily wrapped and also played during the first quarter of Sunday's loss at Denver.
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