Lawrence was injured during a pass-rush drill against left tackle Tyron Smith on Tuesday afternoon. Lawrence tried a speed rush around the end, but Smith moved with him and drove the Lawrence into the ground. Lawrence's foot appeared to get caught under him awkwardly, and he uttered a profanity as the play ended.
He stayed on the ground for a few minutes before limping off the field with trainer Jim Maurer. He was then transported off the field on a cart.
He is flying back to Dallas on Wednesday to have surgery on Thursday, a source told ESPN.com's Todd Archer.
"It's tough," defensive coordinator Rod Marinelli said of the loss of Lawrence. "He's a heck of a young player. I thought he was coming along well and all those things, but that's ball. Just get him ready to go when he's healthy and the next man up. We've got some guys who can come in and still rush over there."
The Cowboys wanted Lawrence to be a major part of their defense as a rookie, which is one of the reasons they moved up to get him in the draft. He was competing with Jeremy Mincey for a starting position.
Marinelli said the Cowboys would look at using strongside linebacker Kyle Wilber, a defensive end until an emergency move due to injuries last season, as a nickel pass rusher to help replace Lawrence.
"His attitude ... you can't discourage him," owner Jerry Jones said of Lawrence on Tuesday. "Physically, his hands, his quickness, his athletic ability, but basically the fact that he doesn't get discouraged. Matter of fact, if he's blocked, he's that much more tenacious, and that may be the quality to have, other than athletic ability as a pressure player."
The Cowboys released DeMarcus Ware this past offseason, and they hoped Lawrence could help compensate for his absence. The Cowboys had just 34 sacks last season, which tied for 25th in the NFL. George Selvie led the team with seven, which doubled his career total. Defensive tackle Henry Melton, coming off a torn ACL, is the most accomplished pass-rusher on the team with 15.5 career sacks.
ESPNDallas.com's Tim MacMahon contributed to this report.