New York's Eric Young hit a grounder in the eighth inning that bounced off the chest of first baseman Freddie Freeman.
Freeman quickly picked up the ball and threw it to Hudson as he raced to cover first base. As the Atlanta pitcher planted his right foot on the bag, Young stepped on Hudson's ankle.
Hudson's foot was dramatically twisted and he collapsed in pain. Those attending Hudson strapped his legs together to ensure his right ankle would not move and he was then placed on a stretcher and lifted onto a cart.
Atlanta officials revealed the extent of the injury after the game and said Hudson would have surgery when swelling in the ankle subsides. The 38-year-old Hudson is due to become a free agent at the end of the season.
Hudson (8-7) wound up winning his fourth straight start, giving up two runs on four hits with a season-best nine strikeouts over 7 2/3 innings.
Atlanta opened the scoring on a home run by Evan Gattis in the second and the Braves broke it open with a five-run fifth. Dan Uggla hit a three-run homer in the big inning and Andrelton Simmons had a two-run shot.
Jeremy Hefner (4-8) surrendered six runs on six hits in 4 1/3 innings to take the loss.