Mayo, 29, was injured in Saturday's victory over the Kansas City Chiefs.
Mayo played in all 16 regular-season games and totaled 49 tackles and one sack.
New England will play the Denver Broncos on Sunday for a spot in Super Bowl 50. The Patriots are attempting to be the first team to repeat as NFL champions since they did it in 2003-04.
AP NFL website: www.pro32.ap.org and http://twitter.com/AP-NFL