Graham, the 13th overall pick in this year's draft, tore his anterior cruciate ligament in 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 says he doesn't need surgery at this time.