The forward was injured during a 4-3 loss at the New York Islanders on Saturday. He played 22:29 and was on the ice when Islanders forward Zach Parise scored 39 seconds into overtime.
Laine has four points (two goals, two assists) in eight games. He missed six games earlier this season after sustaining a sprained right elbow against the New Jersey Devils on Oct. 12 that was expected to keep him out 3-4 weeks.
"It's a tough situation, adversity is going to happen," said Boone Jenner, who is the Blue Jackets captain and Laine's linemate. "Obviously, very unfortunate for him just coming back from an injury, and it happens again. You can't plan for that.
"It's just unfortunate, but it's time for us to get even tighter as a group. It's an opportunity for some guys to step up, and everyone needs to play better in his absence."
The Blue Jackets are also missing their top defense pair in Zach Werenski, who was placed on injured reeserve Tuesday and likely will be out for the season because of a dislocated shoulder and torn labrum, and Nick Blankenburg, who is expected to be out 6-8 weeks because of a fractured ankle and high ankle sprain. Each was injured during a 5-2 win against the Philadelphia Flyers on Nov. 10.
Forward Jakub Voracek is out indefinitely because of an upper-body injury he sustained on Nov. 4. Columbus coach Brad Larsen said he's, "not even in the discussion right now."
Forward Sean Kuraly, who has been day to day with an upper-body injury, practiced Monday and was activated from injured reserve Tuesday, ahead of the Blue Jackets (4-9-1) opening a season-long six-game homestand against the Flyers (7:30 p.m. ET; ESPN+, HULU, SN NOW). Defenseman Erik Gudbranson, who missed the loss to the Islanders because of an upper-body injury, also practiced Monday and could play as well.
"It's hockey, and it seems like it's coming in waves with us right now with some key guys," Larsen said. "But what do you do? You've just got to go play."
NHL.com independent correspondent Craig Merz contributed to this report