Baynes, who had been starting in place of injured star Al Horford, suffered a fractured fourth metacarpal in his left hand in Wednesday night's 111-103 loss to the Phoenix Suns. The injury occurred just two minutes into the first quarter after a dunk.
Baynes, 32, is averaging 5.5 points and 4.5 rebounds in just under 15 minutes per game for Boston.
The loss of Baynes further reduces Boston's depth in the middle, where the Celtics already have been dealing with Horford missing the past five games with patellar tendinitis in his left knee.
Before Wednesday's game, coach Brad Stevens said Horford had made some progress and had done some on-court work but that the team was going to remain cautious with him in his recovery.