Beeks was injured in the ninth inning of Tuesday's win over the Baltimore Orioles. He is 1-1 with a 3.26 ERA and one save in 12 appearances this season.
Oft-injured Rays center fielder Kevin Kiermaier left Wednesday's 4-3 win over the Orioles with back spasms in the fifth inning. Kiermaier grabbed his back while running to second base on a double-play grounder in the fourth inning and departed one inning later while batting.
Manager Kevin Cash is hopeful that it will be a day-to-day situation for Kiermaier.
The Associated Press contributed to this report.