Tarasenko, one of the Blues' top scorers, is expected to be sidelined at least six weeks.
St. Louis (46-14-7) is leading in the race for the Presidents' Trophy, holding a two-point lead over both San Jose and Anaheim. The Blues are one of the league's hottest teams, going 7-0-1 this month.
Tarasenko had a goal against the Predators, giving him six points during a five-game streak. The 22-year-old right wing is tied for second on the team with 21 goals.
With Tarasenko out, the Blues hope to see Alexander Steen regain his scoring touch. Steen still leads the team with 30 goals, but only three have come in the last 15 games, including one in Saturday's victory.
The Blues recalled forward Dmitrij Jaskin from the AHL on an emergency basis.
Information from The Associated Press was used in this report.