Gronkowski, who set an NFL single-season record for tight ends with 17 touchdown receptions, had just two catches for 26 yards in the 21-17 loss to the New York Giants in the Super Bowl in Indianapolis last Sunday. His recovery is expected to last 10-12 weeks and end before the Patriots begin organized team activities in the spring.
Messages left for Gronkowski's representatives were not immediately returned.
The All-Pro tight end, a second-round draft pick in 2010 out of Arizona, suffered a high-ankle sprain in the AFC Championship game against the Baltimore Ravens in Foxborough, a 23-20 victory.
Gronkowski's injury and playing status became a major story during an otherwise slow Super Bowl week.
He was listed as questionable on Friday, 48 hours before the game. He had worn a walking boot for a week before shedding it the Monday before the Super Bowl.
He said he had been making progress every day, but he participated in just one practice, on the Thursday before the game, and that was on a limited basis.
"I felt like I was close," Gronkowski said. "But close isn't there."
During the regular season, Gronkowski had 90 receptions for 1,327 yards with 21 of those catches gaining more than 20 yards. He had three touchdowns in a seven-point win over Indianapolis and three more in a 45-10 divisional playoff victory over Denver,
He and Hernandez combined for 169 receptions and 24 touchdowns as the Patriots went 13-3 and won the AFC East. Gronkowski had started every regular-season game and was healthy for nearly every practice before the ankle injury.
At 6-feet-6 and 265 pounds, also emerged as an outstanding blocker.
Gronkowski joined the Patriots after missing the entire 2009 season at Arizona following back surgery. In his two college seasons, he set school career records of 75 catches and 1,191 yards receiving.