Quinn fractured his left hand during one-on-one pass rush drills during Tuesday's practice but executive vice president Stephen Jones said he expected the pass-rusher to be ready for the Sept. 8 regular-season opener against the New York Giants.
"The relief is he's going to be back and he's going to be fine," Jones said. "He'll be able to get his work in and do what he needs to play the Giants. I don't think we're looking at him missing any [regular-season] time here."
Quinn appeared to sustain the injury while competing against left tackle Tyron Smith. It was not clear whether he got his hand caught in Smith's face mask or elbow brace. He was inspected by the team's head athletic trainer, Jim Maurer, before heading to the locker room for further examination.
Jones said running back DeMarco Murray had a similar injury in 2014 and did not miss a game. Quinn's camp had been going "great," according to Jones. The Cowboys acquired the veteran in a trade from the Miami Dolphins in March.
With DeMarcus Lawrence (shoulder) and Tyrone Crawford (hip) not practicing, Quinn had been working with the first team since the offseason program. He is scheduled to have surgery Wednesday in Dallas.
The Cowboys projected Quinn as a pass-rush specialist, especially with Randy Gregory suspended indefinitely. Gregory has not filed for reinstatement.
Quinn has 69.0 sacks in his career and had 6.5 for the Dolphins last season.
Without Quinn, Lawrence and Crawford, the Cowboys will hope former first-round pick Taco Charlton can improve. Last year's fourth-round pick, Dorance Armstrong, has impressed in camp. The Cowboys also added veteran Kerry Hyder in free agency.