The 30-year-old threw a coin at Burnley fans during a Carling Cup tie at Stamford Bridge.
Drogba will miss the games against Newcastle, Arsenal and Bolton.
An FA statement said: “At a Regulatory Commission today, Chelsea forward Didier Drogba was given a three match suspension.
“Drogba admitted a charge of violent conduct.
“The charge related to Drogba throwing a missile into the away section of the crowd after scoring during the League Cup match against Burnley at Stamford Bridge on Wednesday 12 November.
“Drogba will serve the suspension with immediate effect.”