Luiz will now miss Arsenal’s trip to Aston Villa on Saturday through suspension after the FA upheld his dismissal.
The Gunners had appealed the decision, however, on the grounds Luiz’s contact was accidental or, if any was made, minimal.
Arsenal manager Mikel Arteta said he was “very hopeful” Luiz’s red card would be overturned, but the Gunners confirmed on Thursday afternoon their appeal had failed and the 33-year-old will be suspend for one game.
Arsenal said in a statement: “The Football Association have confirmed to us that the red card given to David Luiz on Tuesday against Wolverhampton Wanderers will stand.
“We have worked really hard to overturn David Luiz’s red card. We presented our case to the FA but are disappointed that our appeal has been unsuccessful.
“We accept the FA’s decision and continue our preparations for Saturday’s match against Aston Villa.”