Bouye sustained the injury in Wednesday's practice and he did not practice Thursday, NFL Network's Ian Rapoport reported.
The team announced on Thursday that he would not travel with the team to England for Sunday's game.
Bouye led the league in passer rating (31.6) among NFL corners last year, when he had six interceptions and was named to the Pro Bowl for the first time.
This season he has dropped to 25th (77.0) in passer rating and has one interception in seven games, all as a starter.
Bouye, now in his sixth NFL season, has 13 career interceptions. He played his first four seasons with the Houston Texans.
The Jaguars also announced that cornerback Tyler Patmon will not travel to London because of a neck injury.
The Jaguars have the league's best passing defense (179.7 yards per game), but with those two cornerbacks out, the Jaguars must hope they can get pressure on Eagles quarterback Carson Wentz.
Rookie corners Quenton Meeks, Tre Herndon and Dee Delaney are expected to get significant playing time against the Eagles in Wembley Stadium on Sunday.