Crawford injured his knee in the fourth quarter of Sunday's 28-17 loss to the Arizona Cardinals.
Crawford, 24, has started all nine games for the Cowboys. He has recorded 20 tackles, and according to ESPN, ranks second on the Dallas defense in quarterback pressures.
The Cowboys are 6-3 this season, while the Jaguars hold a 1-8 record after a Week 9 loss to the Cincinnati Bengals.
After the Cowboys' game Sunday in London, the team has its bye week. The Cowboys' next game after its bye is Nov. 23 against the New York Giants.
According to Todd Archer of ESPN.com, "if Crawford can’t play, then Henry Melton would likely return to the starting lineup, and Davon Coleman (who has not played since September) would likely move into the defensive line rotation."