The incident was not caught by referee Mike Dean, but has been the subject of retrospective action after it was picked up by video footage.
A statement from the FA said: "Ramires receives a four match ban which will start with immediate effect. The ban includes three games for this offence plus an additional game for his sending off at Villa Park last month."
Ramires will miss games against Liverpool, Norwich City and Cardiff City, as well as the Blues' opening game of the 2014-15 season.
Manager Jose Mourinho could also face punishment after he was charged for sarcastically congratulating match official Dean and referees' boss Mike Riley, while assistant coach Rui Faria could also be banned after his angry outburst on the touchline during the game.