The Swede was hit in the hand blocking a shot late in the game Thursday against L.A. A decision on whether surgery is required has yet to be determined.
"It's unfortunate," Sens head coach D.J. Smith said. "I thought he played some good games. He moved the puck well but it's one of those freak things."
In two games this season with Ottawa, Brannstrom was pointless while averaging 16:54 a night. The 22-year-old has also played nine games with Belleville where he scored once and added two assists before he was recalled by Ottawa on Nov. 7.