Conrad was hitting .172 with two home runs and seven RBIs in 24 games.
The Rays felt like they needed an extra reliever to help replenish the bullpen following Monday night's 15-inning contest.
"Right now, obviously after last night we're really concerned about the bullpen," Rays manager Joe Maddon said. "We've been in really good shape, and we're still in really good shape, but now is when you don't want to beat people up."
Maddon said when he talked with the front office everybody agreed that the Rays weren't "going to the dance without those guys being well and rested."
"The moment you start beating up the bullpen too badly, that's the part that's almost impossible to reproduce," Maddon said. "So, we thought we needed that extra arm to be protected."