Manager Kevin Cash said there was no timetable for how long the 30-year-old lefty would be away.
"We fully support Ryan, his thoughts," Cash told Tampa Bay media. "I think it's best just to leave it at that."
Sherriff made his season debut Friday night, giving up two hits while getting one out in a 6-4 win over Miami. The Rays made the move with Sherriff before Saturday night's game against the Marlins.
Sherriff pitched 10 games for the Rays last season, going 1-0 with a 0.00 ERA in 9⅔ innings. He pitched two hitless innings in the World Series.
The Rays selected catcher Joseph Odom to take Sherriff's roster spot.
Sherriff pitched for St. Louis in 2017-18 and then missed a full season after having Tommy John surgery.