Cavani made the post after scoring against Southampton on November 29th.
The forward deleted the post soon after and issued an apology.
He was charged with using insulting and/or improper words, and pleaded guilty to the FA charge.
On Thursday, it was confirmed he would be issued with a three-game ban, effective immediately.
The United forward will now miss the New Years’ Day game against Aston Villa in the Premier League, as well as the Carabao Cup semi-final against Manchester City and the FA Cup third-round game against Watford.
United issued a statement shortly after the punishment was handed out and accepted the ban, while supporting Cavani.
The club’s statement also noted: “The club trusts that the independent Regulatory Commission will make it clear in its written reasons that Edinson Cavani is not a racist, nor was there any racist intent in relation to his post.”
And the striker took to Instagram to explain his meaning behind the post, and apologised to anyone who was offended.
“Hello everyone, I do not want to extend much in this uncomfortable moment for me,” he wrote.
“I want to share with you that I accept the disciplinary sanction knowing that I am foreign to English language customs, but I do not share the point of view.
“I apologise if I offended someone with an expression of affection towards a friend, nothing further was my intention.
“Those who know me know that my effort is to always seek the simplest joy and friendship!
“I appreciate the countless expressions of support and affection.
“My heart is at peace because I know that I always expressed myself with affection according to my culture and way of life. I send you a sincere hug.”