The infection was caught early enough that Gronkowski is not expected to miss any extended time, according to those familiar with the surgery. The two-time Pro Bowler is expected to be ready for training camp.
Gronkowski has had his left arm operated on three times since originally breaking it on Nov. 18 against the Indianapolis Colts. He missed five games and returned for the regular-season finale but broke the arm again on Jan. 13 in a divisional-round playoff game against the Houston Texans.
The 23-year-old Gronkowski was widely criticized earlier this month, when he was videotaped performing a wrestling move on a friend at a Las Vegas nightclub despite having the broken forearm in a cast.
Patriots veteran offensive lineman Logan Mankins later downplayed the incident, claiming that he did not have a problem with Gronkowski "having fun."
Information from ESPNBoston.com's Mike Reiss was used in this report.