The 33-year-old said that a disagreement with his position coach led to his suspension, according to Jordan Schultz of ESPN.
The Athletic's Nick Underhill reported the three-time Pro Bowler let his coaching staff know he wasn't happy with his role.
Bennett signed a two-year, $16.75-million contract with the reigning Super Bowl champions in April after one season with the Philadelphia Eagles.
Coming off a season-low 11 snaps played in New England's Week 6 matchup with the New York Giants, Bennett's 130 snaps in 2019 (35.7% of the Patriots' defensive plays) are ranked 16th on the team.
He's posted 2.5 sacks in six games this season.