McCoy, a six-time Pro Bowl selection, suffered the injury just minutes into the Cowboys' first padded practice of training camp. According to the team, he was injured during individual drills and was unable to put any weight on his leg.
"That's why you have to have a deep roster," Cowboys executive vice president Stephen Jones told reporters Monday. "Obviously why you sign a guy like Everson Griffen. You never know when things like this are going to happen. It's certainly disappointing.
"First and foremost we're disappointed for Gerald. I know he was fired up about being here. But also, it's disappointing for us. He was one of our major acquisitions here in the off-season and free agency. But having said that, this will give Trysten Hill and [Neville] Gallimore an opportunity to really step up now."
The Cowboys signed McCoy to a three-year, $18 million contract earlier this off-season and viewed him as a key part of their defensive line. Dallas also added Aldon Smith, Dontari Poe and Everson Griffen, who has yet to practice with the team but has cleared the NFL's COVID-19 testing protocol.
The Tampa Bay Buccaneers selected McCoy with the No. 3 overall pick in the 2010 NFL Draft out of Oklahoma. He spent his first nine seasons in Tampa Bay before joining the Carolina Panthers last season.
McCoy has missed more than three games in a single season only once in his professional career. He has recorded 334 total tackles, 59.5 sacks, six forced fumbles, four fumble recoveries and 23 passes defensed in 139 career games.