Drogba threw a coin at Burnley fans during his side’s Carling Cup fourth-round tie at Stamford Bridge on Wednesday.
A statement said: “Chelsea striker Didier Drogba has been charged with violent conduct.
“Drogba is alleged to have thrown a missile into the away section of the crowd after scoring during the League Cup match at Stamford Bridge.”
An FA spokesman added: “Players should be able to play football without fearing for their personal safety. It is totally unacceptable for players to be put in danger by supporters throwing missiles onto the pitch.
“The priority now is to work with the clubs and the police to identify the individuals involved.
“The FA wants anyone found guilty of throwing missiles to face the strongest possible action. That includes life bans from attending football matches.”