Hudson said he has noticed the soreness in his last few starts and it has gotten progressively worse. But until Tuesday he was able to pitch through it.
"I've always had soreness in there," Hudson said. "With my arm action I just kind of figured it came with the territory."
Manager Kirk Gibson said Hudson had never told the D-backs about any trouble he was having with his elbow.
"We were unaware his elbow was sore," Gibson said. "That's certainly something that's alarming."
Hudson will return to Phoenix for an MRI on Wednesday.
While the D-backs won't know the extent of Hudson's injury until after the MRI, they will likely have to make a move to shore up their bullpen before Wednesday's game. They used four relievers to get through 6 1/3 innings on Tuesday, including long man Josh Collmenter's second four-inning outing in five days.
"We'll have to have a conversation about what we're going to do," Gibson said. "We're a little short."
Right-hander Patrick Corbin was scratched from his start at Triple-A Reno on Tuesday and could be called up. Corbin made his Major League debut filling in for Hudson in the rotation when he went on the disabled list in April.
Other options could include right-hander Joe Martinez or left-hander Joe Paterson. Both briefly pitched for the Diamondbacks earlier this year before being sent back to Reno.
Teddy Cahill is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.