After the team announced that its first-round pick will miss four to six weeks, Cowboys owner Jerry Jones questioned whether Bryant should have been participating so late in Friday's practice session.
Bryant was injured on the second-to-last play of practice in the Alamodome.
"It was really disappointing and it really causes you to ... ask what can you do, what can you do in practices that can mitigate some of the exposure to some of these injuries," Jones told ESPN's Chris Mortensen after watching footage of the injury. Jones did not attend Friday's practice.
Jones told Mortensen that Bryant might have been tired after a heavy workload, which included returning kickoffs and punts and running numerous routes with the first and second teams all week.
"The key thing is you ask yourself, 'Are we pushing him too hard; does it happen at the end of practice when the players are tired?' " said Jones, who added, "We all know now when you get a little tired you can get injured."
At practice earlier this week, Bryant tweaked his ankle and missed one or two reps while getting it retaped.
An MRI exam confirmed the team's fear of a high ankle sprain. Cowboys vice president Stephen Jones had expressed hope that Bryant, who had a spectacular start to training camp, would be out for only a few days or a week.
The Cowboys' top three picks are injured. Second-round linebacker Sean Lee has been sidelined since Tuesday with a strained quadriceps. Fourth-round safety Akwasi Owusu-Ansah, who had shoulder surgery in March, has not been cleared to practice yet.
"You hate for that to be, but I think Lee is close to being back," Stephen Jones said. "It's a long process and we have a long ways to go before the most important thing, and that's the Washington Redskins [in the Sept. 12 season opener]. You never like it when someone gets nicked or injured."
Bryant's injury occurred after cornerback Orlando Scandrick broke up a pass intended for Bryant. Backup quarterback Jon Kitna threw the ball slightly behind Bryant on a crossing route, and Scandrick made a good play on the ball and landed on Bryant's leg.
Bryant, whom the Cowboys selected with the 24th overall pick after trading up three spots in the draft, stayed down on the Alamodome turf for several seconds. He tried to limp off the field, then went back down before being helped off the field by athletic trainers Jim Maurer and Britt Brown.
"I guess he just rolled his ankle," Scandrick said. "I batted the ball away. I was just competing for the ball and I think his ankle was already bothering him a little bit."
Bryant starred during the first several practices of training camp, making the Cowboys hopeful he could be a major contributor for a unit that was second in the NFL in total offense last season. He has made several spectacular plays and has displayed a decent grasp of the playbook despite missing a handful of offseason workouts with a variety of physical ailments.
Bryant will miss valuable practice and playing time as he tries to recover from his injury.
"You don't like them to miss," Cowboys coach Wade Phillips said. "We do have an extra week [of training camp], which [Bryant] has taken advantage of, being here and learning all those things. He's actually done real well as far as assignments are concerned."
"You're always concerned. It's the nature of our game," offensive coordinator Jason Garrett said of Bryant's injury. "It's a very physical game and that happens a lot."
Tim MacMahon and Calvin Watkins cover the Cowboys for ESPNDallas.com. ESPN.com's Matt Mosley contributed to this report.