Manager Kevin Cash said Fairbanks texted that he was feeling better than he did when he left the ballpark Sunday, though he was still sore. He is scheduled for more tests Tuesday.
"We're not going to replace Pete," Cash said. "He's really, really good. What he does at the back end of the bullpen when he's right and healthy is pretty special. We feel like we do have some guys that can provide some help, and if we can continue to score runs at the clip we are now, that'll help too."
Fairbanks has five saves in six chances and a 1.54 ERA in 13 appearances. He spent time on the 15-day injured list earlier this month because of right forearm inflammation.
The Rays, who owned a 39-16 record entering Monday's game against the Chicago Cubs, recalled right-hander Trevor Kelley from Triple-A Durham. Kelley, 30, is 0-1 with a 5.40 ERA in six appearances (two starts) for the Rays this season.