The Patriots are uncertain exactly how long he will be out, but one source said he expects Gronkowski to miss "probably a few weeks." Before the surgery, an NFL.com report cited Gronkowski as telling people he would be out four to six weeks.
Gronkowski broke his forearm at the end of Sunday's 59-24 rout of the Colts, suffering the injury on the Patriots' final extra point with 3:55 remaining in the fourth quarter, a source said.
Asked for an update Monday on Gronkowski, coach Bill Belichick said, "I don't really have anything. I know that our medical people are looking at all the players today when they come in, trying to assess their situation, like we always do on Monday. I'll catch up with them as they've had a chance (to gather that information)."
When a reporter pressed Belichick on why Gronkowski still was playing special teams late in the fourth quarter, especially since he has been listed as questionable on the injury report, Belichick provided his thinking.
"It's one of his roles and jobs at the game," he answered, before touching on his view on the importance of protection on the field-goal unit. "Whoever does it, it's very important."
Defensive end Rob Ninkovich did not believe it was a mistake for Gronkowski to be in on the extra point attempt, stressing that injuries are a part of football.
"That's football, you're playing football (for four) quarters, and that's the way things go," he said. "You can't really second guess anything, that's just the way football is. People get hurt. You've just got to deal with it."
X-rays after the game revealed Gronkowski's broken forearm.
"I knew he had gotten injured, but I obviously didn't know the extent," quarterback Tom Brady said on his weekly appearance on WEEI sports radio in Boston. "But he's such a great player, it sucks that he gets hurt, but it's part of this game. He's got to do his best to get back as soon as possible, and we've got to go out there and win some games without him."
Fellow tight end Aaron Hernandez, who has missed six games this season with an ankle injury, said Monday that he has exchanged text messages with Gronkowski and that the rest of the Patriots offense must step up in his absence.
"Obviously, it's tough," Hernandez said. "He's one of the best players in the league, but we have a lot of players and everyone has to step up to fill the void."
Hernandez also believes that Gronkowski's absence will impact some elements to the Patriots' offensive approach.
"It will change some things," he said. "Like I said, everyone has to step up and whatever the change is, we've just got to make plays and fill that void that we're going to be missing."
Hernandez said that the confidence level of the tight end group for the Patriots will not be deterred due to Gronkowski's injury.
"The way this program is, the way (coach) Bill (Belichick) makes us become the players that we become is we all have confidence and we all know we have to come to play every game regardless," he continued. "And in the NFL, people go down and other people have to step up."
Belichick said Monday that a decision on whether Hernandez will be available for Thursday night's game against the New York Jets will be made later in the week.
Gronkowski has followed up his record-setting season in 2011 with another strong campaign in 2012, collecting 53 catches for 748 yards and 10 touchdowns through 10 games. He had seven receptions for 137 yards and two touchdowns in Sunday's win against Indianapolis.
The Patriots have leaned heavily upon Gronkowski in the absence of Hernandez. Entering Week 11, Gronkowski had been on the field for 668 of the team's 710 offensive snaps (94.1 percent), the highest total among the team's offensive skill position players.
Gronkowski had 90 catches for 1,327 yards and a tight end-record 17 touchdowns last season.
The Patriots will visit the New York Jets on Thursday night, when they will look to build upon their AFC East division lead.
Information from ESPN NFL Insider Adam Schefter, ESPNBoston.com's Field Yates, Mike Reiss and The Associated Press was used in this report.