Barbashev suffered the injury during the third period of the Blues' 3-2 overtime win against the San Jose Sharks on Feb. 18. He will be re-evaluated in six weeks.
In addition, the Blues have recalled forward Nathan Walker from the American Hockey League's (AHL) Utica Comets and assigned him to the taxi squad.
Walker, 27, was originally signed by the Blues as a free agent on July 1, 2019. This season, the 5-foot-9, 186-pound forward has recorded two goals and six penalty minutes in four games with the Comets.
Overall, the Cardiff, Wales native has appeared in 17 career NHL games, posting four points (two goals, two assists) and 12 penalty minutes.