Tarasenko sustained the injury during a 4-0 win at the Los Angeles Kings on Thursday. The forward, who had a goal and an assist in the victory, was initially listed as day to day.
The 27-year-old forward leads the Blues with 28 goals and is second with 58 points in 66 games. He was named the NHL's Third Star of the Month for February, when he had 10 goals and 22 points in 14 games.
St. Louis (36-25-7) is in third place in the Central Division, four points behind the Nashville Predators and five behind the Winnipeg Jets. The Blues are four points ahead of the Dallas Stars.