Defender Ivanovic was involved in a flashpoint during the 86th minute of Chelsea's 1-0 victory after Gareth Barry had been sent off for a second bookable offence.
The Serbia international put his arm around McCarthy's neck in an aggressive manner before moving his head towards the Everton midfielder.
Referee Jonathan Moss took no action at the time and the Football Association have also opted against taking retrospective action against Ivanovic, but the governing body have charged both clubs.
"Both Chelsea and Everton have been charged by The FA for failing to ensure their players conducted themselves in an orderly fashion and/or refrained from provocative behaviour," read an FA statement.
"It follows an incident in the 86th minute of Wednesday night’s game at Stamford Bridge.
"Both clubs have until 6pm on 17 February 2015 to respond to the charge.
"Meanwhile, Chelsea’s Branislav Ivanovic will not face any further action in relation to an incident involving Everton’s James McCarthy in the 86th minute.
"In Premier League matches, if an incident has not been seen by the match officials, a three-man panel of former elite referees will be asked by The FA to review it and advise what, if any, action they believe the match referee should have taken had it been witnessed at the time.
"For an FA charge to follow, all three panel members must agree it is a sending-off offence.
"In this instance, the panel did not believe the conduct was worthy of a dismissal."
The news will be a relief to Chelsea manager Jose Mourinho, who threatened to walk out of the post-match press conference after being asked whether he was thought Ivanovic could be in hot water with the FA.
The Portuguese also refused to speak to the media in the aftermath of Diego Costa's three-match ban for stamping on Liverpool midfielder Emre Can.
Mourinho then accused the governing body of double standards for not punishing Manchester United striker Robin van Persie for an alleged elbow on West Ham's James Tomkins during last Sunday's Premier League contest.
The former Real Madrid boss also received a £25,000 fine last month after claiming there was a "campaign" against his side following a 1-1 draw at Southampton in December.
