Cooley had the operation Wednesday. He was hurt in Sunday's loss to Philadelphia.
Cooley is also dealing with a left knee injury. Coach Mike Shanahan says Cooley will meet with a doctor on Sunday to help determine whether the veteran will return this season.
Cooley was one of three offensive players injured against the Eagles. Guard Kory Lichtensteiger tore two ligaments in his right knee and was placed on injured reserve Wednesday. Left tackle Trent Williams has a high right ankle sprain and is expected to miss two to three weeks.
The Redskins promoted guard Maurice Hurt from the practice squad to the active roster. Guard John Malecki was signed to the practice squad.