General manager John Mozeliak made the announcement Monday at Busch Stadium. Wainwright will have surgery later this week.
Wainwright was hurt while batting Saturday in Milwaukee.
This is the second major injury of Wainwright's career. The right-hander missed the 2011 season while recovering from Tommy John surgery.
The Cardinals have made it to the NL Championship Series in each of the last four seasons. They lead the NL Central this year.