Murray suffered a left MCL sprain, and Ware strained his right quadriceps, coach Jason Garrett announced after the game.
Both players are scheduled to undergo MRIs on Monday.
"We'll have to see on both of them. I did talk to DeMarcus and he seemed optimistic he could be out there," owner Jerry Jones said after the game. "We thought DeMarco would be back out there but decided against it."
Jones said he didn't know how to talk about their injuries related to next week's game at Philadelphia, "but what I heard doesn't seem long-term for those injuries."
Ware, the franchise's all-time sacks leader with 115, left the game late in the second quarter after rushing the passer. After a few minutes, he walked to the locker room along with assistant athletic trainer Britt Brown.
Ware was walking fine in the locker room after the game and said he thought he would be OK.
The nine-year veteran never has missed a game during his NFL career.
Murray left the game after a run around the right corner early in the second quarter. The Cowboys featured him in the offense early in the game, with Murray rushing for 29 yards and a touchdown on seven carries and catching two passes for 21 yards.
Durability has been an issue for Murray, a third-year veteran, throughout his NFL career. He missed nine games due to injury in his first two seasons.
Murray entered the day ranked fifth in the NFL with 399 rushing yards, averaging 4.8 yards per carry.
It's not clear if he will miss any games, but Felix Jones played through a similar injury last year for the Cowboys.
Information from ESPNDallas.com's Todd Archer and The Associated Press was used in this report.