The forward was injured in a 4-3 overtime loss to the Philadelphia Flyers on Thursday.
"He's a guy that you can count on in every situation this year," Columbus defenseman Zach Werenski said. "I think he was really finding a stride this season, so that [stinks] to see obviously."
Bjorkstrand leads the Blue Jackets with 21 goals and is tied for third with 36 points. He had a goal and an assist against the Flyers and has 20 points (14 goals, six assists) in his past 17 games.
"It's a big hole to fill," forward Pierre-Luc Dubois said. "He's been a big goal-scorer for us of late and a very good player in general."
Columbus (30-19-13), which has not won in its past seven games (0-3-4), holds the first wild card into the Stanley Cup Playoffs from the Eastern Conference. It had nine players on injured reserve before Bjorkstrand's injury, including defensemen Seth Jones and Ryan Murray; forwards Cam Atkinson and Alex Wennberg; and goalie Joonas Korpisalo.
"This isn't new to us," captain Nick Foligno said. "I don't think anyone's feeling sorry for us, so why should we feel sorry for ourselves? I think that we've put a pretty good brand of hockey together with the group we've had. And in some ways, with all the injuries and the question marks on this team, I think it's a little bit of a motivation for this group that people still count us out even the way we've played.
"We're going through a little bit of a tough time. We're right in the thick of it. We're in a wild-card spot. We're right there, so I don't know what the doom and gloom is."
The Blue Jackets visit the Nashville Predators at Bridgestone Arena on Saturday (8 p.m. ET; FS-TN, FS-O, NHL.TV).
NHL.com independent correspondent Craig Merz contributed to this report
