A league source told ESPN NFL Insider Adam Schefter that Bunkley tore a ligament in his elbow.
Bunkley was injured in Philadelphia's 27-24 win at San Francisco on Sunday night. Reid revealed the extent of Bunkley's injury on his radio show Monday night on WIP-AM.
Bunkley was the 14th overall pick in the first round of the 2006 draft. He had nine tackles this season.
In other injury news, quarterback Michael Vick (ribs), left tackle Jason Peters (knee), cornerback Asante Samuel (concussion) and wide receiver Riley Cooper (concussion) are uncertain for the upcoming game against Atlanta.
Information from The Associated Press contributed to this story.