McGee missed the team's mandatory minicamp and sat out the last two weeks of voluntary organized team activities.
Gruden did not say how McGee was injured, when the surgery occurred or how long he will be sidelined.
McGee, 28, played in all 16 games last season and made 10 starts. He recorded 44 tackles, and is expected to play a prominent role this coming season.
The Redskins signed McGee to a five-year, $25 million contract in 2017 when McGee was a free agent.
He played his four previous seasons with the Oakland Raiders and has made 28 career starts.