Abiamiri got hurt at practice on Tuesday.
Abiamiri, an honorable mention All America at Notre Dame, was taken in the second round of the 2007 draft, but injuries limited him to just 29 games in his first four seasons.
He has four regular-season sacks in four years, plus one in the 2008 NFC championship game.
Abiamiri missed all of last season with a knee injury that required offseason microfracture surgery.
The Eagles' defensive line has struggled with injuries in the first week of training camp. Defensive tackle Mike Patterson is out indefinitely after suffering a seizure on Wednesday and defensive tackles Trevor Laws (hip flexor) and Antonio Dixon (knee sprain) are both out of practice.