Tarasenko was injured Monday against the Vancouver Canucks. He leads the Blues with 36 goals and 71 points in 76 games.
The Blues (46-23-7), who trail the Nashville Predators by four points for first place in the Central Division with two games in hand, are already without second-leading scorer Alexander Steen. Steen missed one game with a lower-body injury and his status for Thursday is uncertain.
St. Louis has six games remaining in the regular season.