The injury occurred when Eric Young Jr. grounded softly to Braves first baseman Freddie Freeman. Hudson ran to cover first and received the throw as Young reached the bag. Most of Hudson's foot covered the base and Young appeared to step on Hudson's ankle as he reached first.
Luis Avilan replaced Hudson on the mound for Atlanta.
Up to that point, Hudson had pitched 7.2 innings of four-hit ball, allowing two earned runs and striking out nine New York hitters. Hudson went into Wednesday's game with a 4.08 ERA on the season.
The Braves announced after the game that Hudson would have surgery back in Atlanta once the swelling goes down.
Brandon Beachy is close to a return for Atlanta, and could potentially be ready to go for Hudson next start should he require a DL stint.