Bobrovsky was injured Tuesday while making a spectacular glove save on Tampa Bay's J.T. Brown during the third period of the Blue Jackets' 1-0 victory over the Lightning.
The reigning Vezina Trophy winner had to be helped off the ice and was replaced by Curtis McElhinney, who is in line to take over the starting spot.
Columbus officially placed the 25-year-old Russian on injured reserve to clear a roster spot.
Bobrovsky has posted a 2.72 goals against average and a .909 save percentage this season while going 10-11-2 in 23 outings.
He was named the NHL's top goalie last season, after going 21-11-6 with a 2.00 GAA, .932 save percentage and four shutouts over 38 games.