Miller will be placed on injured reserve and have surgery later in the week, the team said Tuesday.
Miller suffered the injury during the Jaguars' 33-16 loss to Oakland at EverBank Field on Sunday. The 29-year-old Miller started every game for the Jaguars (2-4) this season and has 10 tackles.
Miller has recorded 105 tackles and five sacks in four seasons with the Jaguars. He spent the first four years of his career with the Tampa Bay Buccaneers, where he had 141 tackles and three sacks. The Bucs drafted him in the third round in 2009.