The team made the announcement Sunday, a day after Cobb struck out five in seven innings in Tampa Bay's 1-0 victory over the Cincinnati Reds at Great American Ball Park. He's 1-1 with a 1.89 ERA and 14 strikeouts this season.
Left-hander Jeff Beliveau was promoted from Triple-A Durham to take Cobb's spot on the roster.
"I'm not exactly sure when it happened," Rays manager Joe Maddon told reporters in Cincinnati. "We thought it could have been dehydration."
Cobb's injury places further strain on the Rays' rotation. He makes the third Tampa Bay starter to be placed on the DL, following right-hander Jeremy Hellickson (elbow) and left-hander Matt Moore (elbow). He felt tightness during his start Saturday, but the condition wasn't considered serious at the time.
After the game, Cobb returned to Florida for an MRI. It's predicted he could miss one or two starts.
Left-hander Erik Bedard will be a favorite to replace Cobb as a starter. Bedard was a competitor for the fifth rotation spot in spring training that eventually went to right-hander Jake Odorizzi. Bedard began the season with Triple-A Durham.