The Uruguayan striker sent the message after scoring the injury-time winner in United’s 3-2 win at Southampton.
Cavani, 33, subsequently deleted it and apologised when the meaning that could be attached to it was pointed out.
Under new FA guidelines agreed in the summer, Cavani risks a minimum three-match ban if he is found guilty.
“It is alleged that, contrary to FA Rule E3.1, a comment posted on the Manchester United FC player’s Instagram page was insulting and/or abusive and/or improper and/or brought the game into disrepute,” said the FA in a statement.
“It is further alleged that the comment constitutes an “Aggravated Breach”, which is defined in FA Rule E3.2, as it included reference, whether express or implied, to colour and/or race and/or ethnic origin.”
Cavani has until Monday 4 January 2021 to provide a response to the misconduct charge which United say they will consider, but repeated their message that they are committed to the fight against racism and stressed there was no malicious intent behind the forward’s post.
“Manchester United and all of our players are fully committed to the fight against racism and we will continue to work with the FA – along with other governing bodies and organisations, and through our own campaigns – in that regard,” said United in response to the charge.
“We note the FA decision today to charge Edinson Cavani for his social media reply to a friend’s message of congratulations following the Southampton game.
“Edinson and the club were clear that there was absolutely no malicious intent behind the message, which he deleted and apologised for as soon as he was informed that it could have been misconstrued.
“The player and the club will now consider the charge and respond to the FA accordingly.”
Cavani issued an apology shortly after posting the message on Instagram following United’s win on 29 November.
“It was intended as an affectionate greeting to a friend, thanking him for his congratulations after the game,” said the former Napoli and Paris St-Germain striker.
“The last thing I wanted to do was cause offence to anyone.
“I am completely opposed to racism and deleted the message as soon as it was explained that it can be interpreted differently.”