Steen, who is second in the NHL with 24 goals, hasn't played since he left a game against Edmonton last Saturday with what the team called an "upper body injury."
Blues general manager Doug Armstrong said in a statement that Steen will be out indefinitely.
Steen is the Blues' leading scorer with 38 points in 35 games.
The six-foot, 212-pound forward has six game-winning goals, second most in the league, and is 12th among forwards with a plus-15 defensive rating.
Currently in his ninth NHL season, Steen has 341 points (147 goals, 194 assists) and 248 penalty minutes in 572 career games with Toronto and St. Louis.
Steen, a Winnipeg-born Swede, signed a three-year $17.4 million contract extension with the Blues earlier this month.