Assistant coaches Ray Bennett and Nolan Pratt will take Bednar's place on the bench, the team tweeted. The Avalanche play in Dallas on Thursday night and host the Stars on Saturday.
The Avalanche also will be without backup goaltender Pavel Francouz for approximately three to four weeks due to a lower-body injury. Francouz missed last season after having hip surgery.
Colorado opens the regular season Wednesday against the Chicago Blackhawks.