According to a report on Comcast SportsNet New England, Gronkowski has a broken forearm.
"He left the game with an arm injury," Patriots spokesman Stacey James said about 21/2 hours after the game. "There was no update to that."
Gronkowski had seven catches for 137 yards. He reportedly was injured while blocking for an extra point on the Patriots' eighth touchdown.
Brady threw three touchdown passes for the Patriots (7-3), who scored on two interception returns and a punt return as they extended their winning streak to four. Indianapolis (6-4), which had won four in a row, led 14-7 in the second quarter.
It was the Patriots' most complete win in a season in which they've averaged 35.8 points and lost their three games by a combined margin of four points. The 59 points equals the team mark set against the Titans Oct. 18, 2009.
Gronkowski had 10 touchdown catches as a rookie and then set a record for tight ends with 17 touchdowns last season, when he caught 90 passes for 1,327 yards. But he sprained his left ankle in the AFC Championship Game and was a nonfactor in the Super Bowl, a 21-17 loss to the Giants.
The Patriots have been without Aaron Hernandez, their other first-string tight end, for the last three games after he sprained his right ankle in Week 2. He has just 17 catches for 143 yards and two touchdowns in four games.
Hernandez went from being listed as "out" in the injury report to "questionable" after the Nov. 4 bye week and remained that way for each of the last three games. He had limited participation in practice in each of the last three weeks; the team has not given a timetable for his return.
The Patriots made no announcement about Gronkowski's injury when he headed for the locker room with about 4 minutes left in the game.
Several hours after the game, James said he had no information; inquiries to the NFL media relations department were referred back to the Patriots, who then said Gronkowski had an arm injury.
According to the NFL's media policy, "Team personnel are responsible for reporting in-game injury information factually and accurately as soon as possible for the benefit of the television audience and other media covering our games.
"Clubs must ensure that all medical information issued to the media is credible, responsible, and specific in terms that are meaningful to teams, media, and fans," says the policy, which goes on to remind teams that "the injury reporting policy relates directly to the integrity of the game."