Ware, who started 134 consecutive games before Sunday, is missing the first game of his NFL career.
Cowboys starting running back DeMarco Murray also is inactive because of a sprained knee.
Ware has missed only one start in his career, a 2009 game against the New Orleans Saints, when he started the second half.
Ware suffered the thigh injury in last week's victory against the Washington Redskins.
Kyle Wilber will replace Ware in the Cowboys lineup.
The Cowboys are keeping Ware out of the lineup more as a precaution. Cowboys owner/general manager Jerry Jones said if this were a playoff game, Ware would play.
There is an expectation that Ware could play next week against the Detroit Lions.
A source said Ware could miss three to four weeks, but the Pro Bowl defensive end dismissed that, claiming he didn't know where that report came from.