Late in the second quarter, Owens caught a pass from Tony Romo and the leg was bent behind him awkwardly while being tackled by Carolina linebacker Jon Beason. He left the contest under his own power and did not return.
The injury likely means Owens will miss next week's regular-season finale at Washington.
"This weekend's results give me a great feeling of pride in the job that has been done by our players and our coaching staff," Cowboys owner Jerry Jones told the Fort Worth Star-Telegram after the news about Owens' injury and Green Bay's 35-7 loss to the Chicago Bears.
The Packers can do no better than tie Dallas for the best record in the NFC, and the Cowboys own the tiebreaker because they beat Green Bay 37-27 Nov. 29.