The 29-year-old Stastny was injured in the second period of a 4-3 victory in Vancouver on Friday. He has a goal, four assists and a plus-four rating in five games.
The team placed Stastny on injured reserve Wednesday and said the injury will be re-evaluated in five weeks.
Stastny was hampered by a shoulder injury last season, his first with the Blues. He had 46 points in 74 games.