Shaw hasn't played since January 13. Prior to going down, the 26-year-old Belleville, ON native had amassed 10 goals and 19 points in 43 games so far this season.
Two other injured players didn't accompany the team to St. Louis, including Phillip Danault, who is out with concussion-like symptoms, and Shea Weber. The pair is sidelined indefinitely.
The Canadiens will play the Blues on Tuesday night at Scottrade Center.