Yunel Escobar, out a week due to a sore shoulder, was placed on the 15-day disabled list after Monday's win in New York.
The team will make a corresponding move Tuesday.
Rays manager Joe Maddon does not seem concerned that it will be a long-term situation.
"It's a long season. One of his major strengths is his arm strength... why would you want to lose that tool by trying to rush back right now," Maddon said.
Escobar made a large number of throws at Yankee Stadium earlier Monday. Maddon said the injury is "nothing horrid" and that Escobar's "just a little bit concerned" with being able to fully let the ball go.