Kelly was signed in the offseason, started five games and had 2.5 sacks before being injured in Week 5. He was inactive the last three contests.
It's another big blow for the Patriots' defense that is now without its two starting defensive tackles. Vince Wilfork already was placed on IR with a torn Achilles. Starting linebacker Jerod Mayo also is out for the season.
Bill Belichick's defense will have to mix-and-match players and defensive schemes during the second half of the season to make up for the plethora of injuries.