After experiencing discomfort during a throwing session in Oakland over the weekend, Glasnow was diagnosed with right flexor inflammation following an MRI, the Rays announced Monday.
He'll be shut down for the next three weeks, at which point he will be re-evaluated.
Glasnow was off to a red-hot start for the Rays and led the American League in ERA (1.86) when he suffered forearm tightness during a start on May 10. He was placed on the 10-day injured list the following day with a right forearm strain and hasn't pitched in a game since.
The setback is potentially a big blow to the Rays' summer plans, as they had expected Glasnow to be ready to return after the All-Star break, according to Juan Toribio of MLB.com.
Glasnow, 25, struck out 55 batters while walking just nine during his first eight starts this season.
Tampa Bay also got bad news on two other players currently on the IL. Infielder Daniel Robertson underwent arthroscopic knee surgery to remove a loose body and will be out for approximately four-to-six weeks. Reliever Diego Castillo, meanwhile, was diagnosed with a right shoulder impingement and is expected to miss two weeks of action.