Webb was optioned to Triple-A Reno on Friday.
The 28-year-old was added to the big-league roster Wednesday, though he didn't see game action during his brief time in the majors. Webb struggled in five relief outings for Reno after being claimed off waivers by Arizona in April, posting a 12.46 ERA, and he'll continue to travel with the Diamondbacks for now as a member of the taxi squad.