"Upper-body," Bruins coach Bruce Cassidy said. "Will not play tonight. Will not play Saturday. We'll have a better idea, both of them, once we are back in Boston."
Defenseman Torey Krug was also hurt against Carolina on Tuesday and is a game-time decision for Thursday against the Panthers.
The Bruins are already without center Patrice Bergeron (broken foot) and defenseman Charlie McAvoy (sprained knee). At the end of February, the Bruins said that Bergeron would be evaluated in two weeks. McAvoy was ruled out for at least four weeks March 6.
Chara, 40, is the captain of the Bruins, who are currently second in the East with 96 points.