Cavani investigated by English FA over social media post
The 33-year-old Uruguayan striker sent an Instagram post including the Spanish word "negrito" ('black') in reply to a message of congratulations after his brace completed a come-from-behind 3-2 win over Southampton.
United said the word was clearly used in an affectionate manner and has different connotations in South America.
The club said the former Paris Saint Germain forward had been informed such terms are viewed as derogatory in Britain and he subsequently deleted the post.
The FA issued guidelines pre-season clamping down on racist and discriminatory language and behaviour, with offences on social media carrying a minimum three-game ban.
Manchester City's Bernardo Silva and Dele Alli of Tottenham were both suspended for one match last season after posts that breached the guidelines.