The Tampa Bay Times reported that the right-hander will attempt to pitch through the injury but that Tommy John surgery remains an option.
Earlier Tuesday the Rays said Cobb had experienced a setback in his recovery from a forearm injury, further delaying his return to the team's rotation.
The Rays canceled Cobb's scheduled throwing session Sunday after he "just didn't feel right," according to manager Kevin Cash.
"He just didn't feel as good as he was hoping," Cash told reporters Monday. "Any time you're dealing with a pitcher's arm, it's obviously concerning."
Cash said Cobb, who has been sidelined since March 17 with forearm tendinitis, was examined by team doctors and will be shut down from throwing for at least the next few days.
Cobb, 27, was one of Tampa Bay's best pitchers in each of the past two seasons. He went 10-9 with a 2.87 ERA last year after posting a 2.76 ERA in 2013.