The defenseman was injured blocking a shot in a 2-0 loss to the Los Angeles Kings on Thursday. He was playing his second game of the season after skating 14:52 in a 3-2 loss to the Boston Bruins on Tuesday.
"It's a week-to-week thing for sure," Senators coach D.J. Smith said Saturday. "It's unfortunate. I thought he played some good games, I thought he moved the puck well. It's one of those freak things and we'll move on without him."
Brannstrom scored no points in two games and three points (one goal, two assists) in nine games for Belleville of the American Hockey League. It's not known if he will need surgery.
Ottawa was without nine players against the Pittsburgh Penguins on Saturday because of NHL COVID-19 protocol: goalie Matt Murray; forwards Alex Formenton, Austin Watson, Connor Brown and Dylan Gambrell; and defensemen Josh Brown, Victor Mete and Nick Holden and Nikita Zaitsev.
Zaitsev was removed from protocol Saturday before being placed back in prior to the game.
"We're just going to try and scratch and claw and get ourselves a win," Smith said. "… We're doing everything we can to get through this together and we've just got to give everything we have as well on the ice."
Forward Andrew Agozzino and defensemen Jacob Bernard-Docker and Max Guenette were recalled from Belleville on Saturday. Bernard-Docker made his season debut in place of Zaitsev.
NHL.com independent correspondent Callum Fraser contributed to this report
