Hudson has been on bereavement leave the past four games following the death of his grandmother.
Clippard, who has been a reliever for the past eight seasons, has more experience in the role, having saved 54 games.
Hudson, meanwhile, transitioned to the bullpen last year after having a pair of Tommy John surgeries.
Clippard has been pitching better of late than Hudson, who had a 1.55 ERA before struggling with a 33.00 ERA over his last six appearances.
"I would just assume that Clip slides into Zig's role just based on I've missed a few days here and wasn't exactly throwing the ball fantastic before," Hudson said. "I'm just ready to go get three outs whenever they ask me to."
Steve Gilbert has covered the D-backs for MLB.com since 2001. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.