With the longtime ace out, rookie Jack Flaherty will begin the year in the rotation as the fifth starter.
Wainwright recently hurt his hamstring in a conditioning drill and was scratched from his spring training start Sunday. Closer Luke Gregerson also injured a hamstring during a drill and will be on the DL.
Wainwright, 36, had pitched well this spring and was set to start the second game of the season, on Saturday in New York against the Mets. That slot would have lined him up to pitch the home opener April 5 against the Arizona Diamondbacks.
Wainwright was 12-5 with a 5.11 ERA last year.
Flaherty, 22, made his major league debut last season and went 0-2 with a 6.33 ERA in six games.
The Associated Press contributed to this report.