Hudson exited Tuesday's game in Atlanta in the second inning after complaining of elbow soreness.
A magnetic resonance imaging exam confirmed a tear of the right-hander's ulnar collateral ligament and he was placed on the 15-day disabled list.
The typical treatment for such an injury is "Tommy John" ligament replacement surgery, which usually requires 12 months of recovery time.
Hudson indicated he may seek a second opinion on the diagnosis.
The 25-year-old hurler has struggled this season, going 3-2 with 62 hits and 12 walks over 45 1/3 innings, compiling a 7.35 ERA.
Last season -- his first full year as a major league starter -- saw the Old Dominion product rack up a 3.49 ERA through 222 innings for the D-backs.