The 32-year-old center was injured during practice Sunday. He has points in each of Columbus' two games this season (one goal, one assist) while averaging 14:27 of ice time per game.
Dubinsky had 16 points (six goals, 10 assists) in 62 games last season after coming off surgery to his right wrist. He also missed seven weeks with an orbital bone fracture sustained in a fight with Edmonton Oilers forward Zack Kassian on Dec. 12.
The Blue Jackets play the Colorado Avalanche at Nationwide Arena on Tuesday (7 p.m. ET; FS-O, ALT, NHL.TV).