The right-hander was diagnosed Wednesday with a tear of the ulnar collateral ligament of his right elbow, and was placed on the 15-day disabled list, though he will almost certainly be out far longer than that.
The typical treatment for the injury is ligament replacement surgery -- Tommy John surgery as it's commonly known -- and the recovery from that surgery is typically 12 months.
"That's not good news," D-backs manager Kirk Gibson said. "It is what it is, and he'll have to get it fixed."
Hudson confirmed Wednesday that he will seek a second opinion, which is standard in these situations.
D-backs General Manager Kevin Towers said on KTAR 620 AM that Hudson had a 100 percent tear of the UCL.
Hudson, who was 3-2 with a 7.35 ERA, left his start Tuesday in the second inning with pain in his elbow. After the game he said he had been experiencing soreness during his previous couple of starts, but did not inform the team.
"We were unaware that he had soreness in his elbow," Gibson said. "I guess he had a little soreness in there and he just kind of wrote it off as normal soreness, so I guess last night probably did some more damage to it."
Josh Collmenter will start Sunday against the Brewers in Hudson's place.