The Uruguayan thanked a follower on his Instagram story last month using the phrase "gracias negrito," which translates to "thank you, little Black one."
The phrase is seen as an affectionate term of endearment in South America but considered offensive in other parts of the world, because its meaning can be misconstrued.
Cavani later issued an apology for the language used saying "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."
In a statement on Thursday the FA said the post was "insulting, abusive, improper and brought the game into disrepute" and constituted an "aggravated breach [...] as it included reference, whether express or implied, to colour and/or race and/or ethnic origin."