Cobb pitched seven innings in a 1-0 win over the Cincinnati Reds on Saturday. He's gone 15-1-3 innings without allowing a run.
Left-hander Erik Bedard was added to the roster on Sunday and will take Cobb's spot in the rotation for now.
Left-hander Matt Moore went on the 15-day DL earlier in the week with a sore elbow. The Rays moved left-hander Cesar Ramos from the bullpen into the rotation to take his place - Ramos started Sunday against Cincinnati.
Ramos and Bedard competed for a spot in the rotation during spring training, so they were ready to be starters when the season began.
Cobb felt some tightness in his side during the game on Saturday, but he was throwing so well that the Rays thought nothing of it.
"I'm not exactly sure when it happened," manager Joe Maddon said. "We thought it could have been dehydration."
He was examined after the game and sent back to Florida for an MRI to determine the extent of the problem. The Rays put him on the disabled list right away because they knew he'd miss one or two starts anyway.
"If we do everything right, there's a chance we could have him back for that third start," Maddon said.