The charge relates to incidents involving visiting supporters during the match at The Valley in January, which has now led to formal disciplinary proceedings.
The FA confirmed the action after completing an investigation into reports from match officials and stadium security, focusing on fan behaviour during the fixture.
Although Chelsea secured a convincing 5-1 victory on the pitch, the result has now been overshadowed by off-field issues.
According to the governing body, the club failed to ensure proper control of its travelling supporters, particularly during the second half of the match when concerns were raised about crowd conduct.
"Chelsea FC has been charged for misconduct in relation to its FA Cup fixture against Charlton Athletic FC on Saturday 10 January. It's alleged that around the 56th minute of the match, the club failed to ensure that spectators and/or its supporters (and anyone purporting to be its supporters or followers) didn't behave in an improper, offensive, abusive or insulting way with either an express or implied reference to religion or belief," a statement from the FA read.
Chelsea reached the final but they suffered a 1-0 defeat to eventual winner Manchester City at Wembley.