The incident occurred late on during the Premier League match at Stamford Bridge – which Chelsea won 1-0 – after Everton’s Gareth Barry was sent off for a trip on Willian.
A mass confrontation ensured and Ivanovic grabbed McCarthy around the neck before appearing to move his head towards him. McCarthy was booked his part in the fracas but Ivanovic was not and could face retrospective action.
The FA are awaiting the referee’s report and have two days to decide on what action – if any – to take.
Chelsea manager Jose Mourinho refused to discuss the issue after the match and threatened to walk out of his post-match news conference when asked about Ivanovic’s role.
“I’m concerned with my reaction, because one more question (and) I leave,??? he said.
“And after that, you are not happy. The next question for that story, I have to go.”
However, Everton boss Roberto Martinez was more forthcoming and told his news conference he felt Ivanovic should have been sent off.
“If you look at the images, Ivanovic’s behaviour is wrong. That shouldn’t be allowed,??? he said.
“He grabs James McCarthy around his neck in a very forceful manner, then he puts his head against him when James McCarthy never reacted one single bit.
“If you want to be on top of the laws, that’s a red card. We got nothing out of that moment.”