Doctors put new plates in to repair the previously broken left forearam.
The estimated timetable for recovery is around 10 weeks, assuming there are no setbacks.
Gronkowski originally broke the arm Nov. 18 in a game against the Indianapolis Colts. He returned to action on Dec. 30 in the regular-season finale, then broke the forearm again in the AFC divisional round of the playoffs on Jan. 13 against the Houston Texans.
The forearm surgery may not be the only procedure Gronkowski has this offseason. He will also visit noted spine specialist Robert Watkins in California in three to four weeks to decide whether he needs back surgery, a source told Schefter.
Gronkowski recently had an MRI on his back to further inspect a disk injury he sustained last season.
Information from ESPN NFL Insider Adam Schefter and ESPNBoston.com's Mike Reiss contributed to this report.