Prior to his injury, Hoover was 1-0 with a 4.18 ERA in 31 games.
Delgado suffered the loss in Saturday night's game against the Braves when he allowed four runs in 2/3 inning.
Delgado is listed as having right elbow inflammation.
Staying in his lane With the Trade Deadline looming, D-backs manager Torey Lovullo is staying focused on the team he currently has, not players he might possibly get.
"[General manager Mike Hazen] is taking care of those things," Lovullo said. "I have nothing to do with it. The only way I know it is that the front office takes care of all those areas and I just manage the guys that are here or brought in the clubhouse."