The Boston Herald reported the news less than 24 hours after the third-year pro from Arizona departed his team's 41-28 victory over the Houston Texans in an AFC second-round playoff contest.
Gronkowski left the game in the first quarter and did not return after he landed on the arm while attempting to catch a Tom Brady pass.
It is a recurrence of a similar injury sustained in Week 11, where Gronkowski ended up missing five games following surgery.
