In the top of the sixth inning in the Diamondbacks' 11-4 trouncing by the Braves, the three-time Gold Glove Award winner attempted to catch a wild throw from pitcher Juan Cruz and left the field at the end of the inning holding the wrist.
After his injury, Hudson rolled around and winced in pain for a few minutes.
He did not return and was replaced by Augie Ojeda.
On the team's Web site, Manager Bob Melvin said the injury could require surgery.
"If he has the surgery, he's out for the rest of the year," Melvin said. "If he doesn't, there's still a chance he could be out for the rest of the year."
Hudson was hitting .305 with eight homers and 41 RBI in 407 at-bats.