Buccaneers linebacker Jason Pierre-Paul also did not travel with the team and is out with hand and shoulder injuries. Starting cornerback Carlton Davis (abdomen/ribs) was also listed as questionable.
Gronkowski had been considered unlikely to play, as he was listed as doubtful and did not participate in practice all week, though he was seen at practice Friday during the portion open to the media. Pierre-Paul practiced Friday for the first time since Sept. 15 and had been listed as questionable, though coach Bruce Arians had said that both players would be game-time decisions.
Being out means Gronkowski will miss his first matchup against the Patriots, with whom he spent nine seasons from 2010 to 2018.
Gronkowski has been one of the Buccaneers' most potent red zone weapons this season and has totaled 16 receptions for 184 yards and four touchdowns in three games.
Pierre-Paul has been the emotional leader of a defense that has only three sacks through the first three games.
Information from ESPN's Jenna Laine was used in this report.