Right-hander John Brebbia was recalled from Triple-A Memphis in a corresponding move. Wainwright's placement on the DL was made retroactive to April 20.
Wainwright, who is 1-2 with a 3.45 ERA in three starts this season, was scheduled to start in Tuesday night's game against the New York Mets. The Cardinals have not named a replacement for Wainwright's spot in the rotation.
He tweeted Sunday that "all will be well in a few days."
Wainwright had surgery to shave cartilage down in the elbow in the offseason.
Manager Mike Matheny said Sunday on SiriusXM's MLB Network Radio that it "made sense" to be cautious with Wainwright and make "sure we get ahead of something before it's a bigger issue."