Graham, the 13th overall pick in April's NFL Draft, tore his anterior cruciate ligament during Sunday night's 30-27 win at Dallas.
Philadelphia sent its first-round pick (24th overall) and a pair of third-round selections (Nos. 70 and 87) to Denver to move up and select Graham. He had three sacks.
The Eagles also lost middle linebacker Stewart Bradley indefinitely. Bradley dislocated his right elbow, but coach Andy Reid said Bradley doesn't need surgery at this time and he could return later this season.
Bradley sustained the injury during the second quarter after jumping over a Cowboys player and landing awkwardly on the arm. Rookie Jamar Chaney, mainly a special teams player, replaced Bradley because backup Omar Gaither was inactive for Sunday night's game.
Bradley has been plagued by injuries the past two seasons -- he sustained a concussion in Week 1 and missed the next game. He missed all of last season due to a torn anterior cruciate ligament.
The Associated Press contributed to this report.