The move comes one day after Bennett was inactive in the Patriots' 35-17 win over the Miami Dolphins due to shoulder and hamstring injuries.
New England also put defensive back Nate Ebner on injured reserve.
Bennett caught six passes for 53 yards in two games with the Patriots after the club claimed him off waivers on Nov. 9 following his release from the Green Bay Packers. The 30-year-old intended to undergo season-ending shoulder surgery when the Packers waived him, but he signed with the Patriots instead.
Monday's move could signal the end of the career for Bennett, who openly discussed the possibility of retiring at the end of this season.
Ebner has recorded five tackles on defense to go along with 74 on special teams in 82 career regular-season games. The 28-year-old injured his knee during the first quarter on Sunday while being tackled on a 14-yard run on a successful fake punt.