The Blues said the procedure was successful and the forward will be re-evaluated in four weeks.
Tarasenko, 27, played in 76 regular-season games and recorded 68 points (33 goals, 35 assists) this season. The 33 scores marked the fifth consecutive 30-goal season for the forward.
In the postseason, Tarasenko scored 11 goals and registered 17 points in 26 games. He helped the Blues win their first Stanley Cup championship in franchise history.
Tarasenko didn't miss any games during the NHL playoffs, but he sat out multiple practices toward the end of the postseason. He also played through a shoulder injury during the Stanley Cup Final against the Boston Bruins.
The Blues begin training camp in September.