Gruden said Galette is scheduled to have surgery Friday.
Galette, 27, was released by the New Orleans Saints earlier this summer, less than a year after they signed him to an extension worth up to $41 million.
He was arrested in January on charges of domestic violence, but those were later dismissed. There's also a video from 2013 that shows a man who resembles Galette involved in a fracas on the beach, during which the man strikes a woman. Galette's attorney has denied that the man was his client.
Galette remains under investigation by the NFL and faces suspension.
The Redskins signed Galette earlier this month to a one-year deal, with general manager Scot McCloughan saying the team was "thorough, thorough, thorough" in its investigation of him.
Galette had just returned to full-time work after suffering a torn pectoral muscle in June and was expected to make his preseason debut Saturday at Baltimore. The Redskins were counting on Galette and fellow outside linebacker Ryan Kerrigan to form a strong pass-rush combination this season.
"Right now, I'm worried about him as a person," nose tackle Terrance Knighton said of Galette. "I know he loved the game and he probably feels like he's letting people down, that's how much he cares about his teammates and the people around him and his family. To me right now the impact hurts on a personal level.
"Football-wise, the next guy has to step up. Trent Murphy has been having a great camp. He was definitely ready to start, so he'll be ready. We drafted Preston Smith to come in and be an impact player."
Information from ESPN's Dianna Russini and John Keim and The Associated Press was used in this report.