Television replays showed Costa nuzzling his mouth into Gareth Barry’s neck, but the Everton midfielder insisted the Spain international had not bitten him.
Costa was sent off by referee Michael Oliver for two yellow cards in the FA Cup quarter-final defeat at Goodison Park.
A statement from the FA read: “Diego Costa has been charged in relation to Chelsea’s FA Cup sixth round fixture against Everton on Saturday, March 12, 2016.
“It is alleged his behaviour, after being shown a second yellow card in the game, amounted to improper conduct.
“He has until 6pm on March 17, 2016 to respond to the charge.
“Meanwhile, the Chelsea striker has until Wednesday (March 16, 2016) to provide his observations to the FA in relation to an alleged gesture he made towards Everton supporters while leaving the pitch at half-time.”