Cowboys owner Jerry Jones said Bryant will need surgery to place a pin in his foot and repair the injury that occurred sometime during the third quarter.
"That's a tough loss. You can't replace Dez Bryant," quarterback Tony Romo said. "I hurt for him, right now, because I know how much he loves to play this game.
"You need guys to step up. No one is going to be Dez Bryant, but the guys can do what they do well, and that's my job is to help that whole situation."
A source told ESPN's Todd Archer that Bryant would have the surgery Tuesday.
Bryant, who signed a five-year, $70 million deal with $48 million guaranteed in the offseason, has had at least 88 catches and 1,200 yards each of the past three seasons, while scoring 41 touchdowns in that span.
As his teammates returned to the locker room, Bryant burst out of the locker room, hopping on one foot, jumping and congratulating teammates coming off the field.
Bryant later took to Twitter:
I'll be back soon but how about 9????????#cowboynation— Dez Bryant (@DezBryant) September 14, 2015
Without Bryant, receivers Terrance Williams and Cole Beasley and tight end Jason Witten will likely be the focal points of the passing offense. Devin Street will probably start at Bryant's spot because Beasley works primarily in the slot.
The Cowboys' offense will change without Bryant because he's a player who draws constant double-teams, making it easier for the Cowboys to run the ball. Without him, teams will probably play the run more aggressively and dare the Cowboys to make big plays in the passing game.
"Dez Bryant's a great player," coach Jason Garrett said. "He's one of the best players we have and one of the best in the league and he makes a huge difference for us.
"Sometimes, those guys aren't available to you, so the next guy has to go in there and play, and everyone has to do their job."
The Cowboys should have confidence in their ability to move the ball without Bryant because Romo drove the offense for touchdown drives of 76 and 72 yards in the last five minutes, culminating in an 11-yard, game-winning touchdown pass to Witten with seven seconds left.
They did it without Bryant, which is no different than how the Cowboys spent the offseason. Bryant skipped the club's offseason workouts while he was involved in a contract dispute. He signed his new deal just before the start of training camp but did not play in any preseason games.
"We'll just have to go back and take a look at what we did in the offseason," said playcaller Scott Linehan. "We really worked our depth with Dez not being there in the offseason.
"Terrance stepped up and had some key catches in that situation. Street had a lot of playing time in those situations, so he's a lot more confident."
Information from ESPN NFL Insider Ed Werder and The Associated Press contributed to this report.