The club disclosed the injury on Wednesday.
The veteran was injured late in Tuesday night's 2-1 victory over Calgary when he collided with Flames forward Curtis Glencross. The win gave the Blue Jackets (4-1-0) their fastest start in franchise history.
Hejda's plus-8 rating in five games ties him for the best in the NHL with Dallas' Nicklas Grossman.
Hejda's spot likely will be taken by Mathieu Roy. The Blue Jackets already are down one defenseman as Mike Commodore -- a part of the top pairing on the blueline with Hejda -- recovers from a groin injury.