The Uruguayan international has since abolished the post but could face sanctions by the authorities
The Manchester United striker came off the bench to shoot his side for a 3-2 win over Southampton on Sunday.
The Red Devils were 2-0 when the Uruguay international came off the bench for the second half and forced Bruno Fernandes to pull one off before heading to two of his own to seal the three points deep in the stoppage time .
The 33-year-old shared some of the positive messages he received from fans following the victory and responded to a message with the message “Gracias n ******”.
Objective 50 revealed: the 50 best players in the world
Cavani has since deleted the post.
The term Cavani uses is the same Uruguayan co-star Luis Suarez is said to have used during his altercation with Patrice Evra in October 2011 which resulted in a £ 40,000 fine and the former star’s eight-match ban from Liverpool.
The FA and United have yet to comment on the matter.
Cavani joined the Old Trafford side on a free transfer in October and has scored three goals in five replacement Premier League appearances.
Coach Ole Gunnar Solskjaer praised the striker after his impact in Sunday’s game and was impressed with his movement off the ball.
“He is one of the best because of his experience and his qualities, of this movement,” said Solskjaer.
“He’s one of the best movers you can see. He can get off the shoulder, he can get in front of you, he can pin you.
“He wants to be between the two posts, which I like. I like a center forward that goes in there. It can hurt sometimes but, when you’re there and you get the ball in there, you’ve played and the ball has been thrown, that’s a goal. Two goals!
United captain Harry Maguire went so far as to hail him as an example for other forwards.
“He’s been without a club for a few months so he’s coming in and catching up. He’s a great professional, he’s great to have around the place, he’s great in the locker room and I think you’ve seen today what he brings to the club, ”he said.
“His movement when the ball is wide is at a level that few attackers can achieve. He’s always on the move, always through people and that’s why he’s always scored goals. So if there are any forwards here who want to learn and watch, I’m sure they’re studying his move and what he’s done in his career. ”