The surgery was first reported by the Sports Business Journal.
Gronkowski suffered a high-ankle sprain in the AFC Championship game against the Ravens at home, a 23-20 victory.
A 2010 second-round pick out of Arizona, Gronkowski had 90 catches for 1,327 yards and 17 touchdowns this season.
Gronkowski's injury and playing status became the story during an otherwise slow Super Bowl week. He was listed as questionable on Friday, 48 hours before the game.