The Cardinals recalled Luke Weaver to take Rosenthal's place on the active roster.
Rosenthal has appeared in 50 games, posting a 3.40 ERA and striking out 76 batters in 47.2 innings.
The 27-year-old is coming off a rough outing in Wednesday night's 5-4 defeat to the Boston Red Sox. After entering the game in the ninth, he allowed a solo home run to Xander Bogaerts and walked Mitch Moreland before exiting the game.
The St. Louis Post-Dispatch's Derrick Goold didn't think Rosenthal looked 100 percent on the mound:
Rosenthal's injury comes at a bad time for the Cardinals, who entered Thursday 2.5 games back of the first-place Chicago Cubs in the National League Central. St. Louis is also 5.5 games back of the final wild-card spot in the NL.
According to FanGraphs, the Cardinals bullpen is eighth in collective FIP (3.85), and Seung Hwan Oh has 18 saves this year, so the team isn't without a replacement in late-inning situations.
Still, Rosenthal has been dominant this year, and his absence won't help St. Louis get back to the postseason after missing out in 2016.