Marchand appeared to suffer the injury after getting hit into the boards by Capitals forward Garnet Hathaway. Marchand was seen on the bench grabbing his right shoulder and putting ice on it.
Earlier in the game, Capitals forward Tom Wilson knocked Bruins forward Anton Blidh out of the game with an open-ice hit.
Marchand has 20 goals and 43 points in 31 games this season. Since Jan. 1, the 33-year-old has scored an NHL-best nine goals and 16 points over 10 games.