Davis drew an unsportsmanlike-conduct penalty after he made a touchdown catch, turned and shot the ball into the air, mimicking a basketball jump shot.
The cornerback said he will appeal the fine, a result of a celebration in Sunday's victory over the Cleveland Browns.
Redd's indefinite suspension follows four-game suspension received in November of 2015.
Flagged for unnecessary roughness after officials said he was guilty of a helmet-to-helmet hit, Redskins cornerback Chris Culliver instead was fined for unsportsmanlike conduct.
Redskins rusher has been out since the preseason with an injury.
The NFL has suspended the pass rusher for two weeks as punishment for a January arrest. It will cost him game checks, since he's already on injured reserve.
Washington's defensive lineman is $17,363 lighter in the wallet.
On the same day that they get cornerback Bashaud Breeland back from a one-game suspension, the Redskins learned they will lose cornerback Chris Culliver for the coming game.
Rookie wide receiver Jamison Crowder will not face any discipline from the NFL after a league investigation into allegations of domestic violence cleared him of any wrong doing.
After claiming disparaging remarks by GM’s wife to ESPN reporter were from ‘fake’ Twitter account, Redskins release her statement of apology.