Tensions escalated in front of the Stamford Bridge tunnel after Ross Barkley’s equaliser deep into stoppage time saw Chelsea secure a 2-2 draw on Saturday.
Former Chelsea manager Mourinho was angered by the way Ianni, an assistant to current Blues boss Maurizio Sarri, celebrated in front of the United bench.
Portuguese coach Mourinho leapt from his seat and had to be restrained by security staff as a melee ensued.
Both Ianni and Sarri have since apologised to Mourinho, with the United manager saying he now considers the matter closed.
But the FA, English football’s governing body, has decided to take action.
“Chelsea coach Marco Ianni has been charged following the game against Manchester United on Saturday,” said an FA statement.
“It is alleged that his behaviour in the 96th minute constituted improper conduct.
“In relation to this incident, Jose Mourinho has been formally reminded of his responsibilities whilst both clubs have received similar official reminders in terms of the behaviour expected of their staff and players at all times whilst in the technical area.”
Mourinho, speaking ahead of United’s Champions League match against Juventus on Tuesday, played down the fracas by saying he did not want it to damage Italian coach Ianni’s career.
“I want to thank Sarri for his honesty,” Mourinho told reporters. “I want to thank Chelsea for its honesty too.
“But I’m not happy that it’s going too far with the young boy (Ianni).
“He apologised to me, I accept his apologies. I think he deserves a second chance.
“I don’t think he deserves to be sacked, I don’t think he deserves anything more than the fact that his club was strong with him.
“Everybody makes mistakes, I made a lot of mistakes, so I hope they let the kid go on.”
Mourinho does not face further FA action relating to the incident but is preparing to answer a separate charge of using abusive, insulting or improper language following United’s 3-2 win over Newcastle, relating to remarks he allegedly made in Portuguese.
He has until Wednesday to respond and Mourinho could face a touchline ban if the charge is upheld.