The right-hander went on the 15-day disabled list Saturday with a right shoulder impingement and will stay in Phoenix to work on his rehab at Salt River Fields.
"He hasn't thrown yet, right now it's treatment and strengthening his shoulder to try to get the stiffness out," manager Kirk Gibson said. "We always take our time and make sure they're 100 percent. You don't want to rush him back, even as much as you want to sometimes. I want to make sure they can participate in their regular roles."
Once the D-backs return to the Valley on May 7, Hudson is scheduled to throw a bullpen to evaluate where he is in his recovery.
"That's the initial plan," Gibson said. "That's if everything goes well."