Wainwright, 36, was activated from the DL this past weekend after a bout with elbow inflammation but lasted only 2 1/3 innings Sunday in a start against the San Diego Padres.
"I need to pause and get it right,'' Wainwright said Sunday. "This team deserves more than that, and the fans deserve more than that, and the organization does, too. If I'm going to be a force down the stretch, I need to get healthy first. Luckily, we have a lot of young guys primed for this position.''
One of those young pitchers, 22-year-old Jack Flaherty, was recalled from Triple-A Memphis and will start Tuesday against the Minnesota Twins.
Wainwright is 1-3 this season with a 4.00 ERA in four starts. Flaherty has made two starts this year, going 0-1 with a 3.60 ERA.
Information from The Associated Press contributed to this report.