Fofana, 25, picked up a second yellow card in the 72nd minute with Chelsea leading 1-0 against Burnley at Stamford Bridge.
The centre back has since taken to social media to call out those who racially abused him after the game.
Chelsea have since released a statement backing Fofana, saying the club are “appalled and disgusted” by the abuse.
The statement says: “The targeted racist abuse Wes has been subjected to following today’s Premier League fixture against Burnley is abhorrent and will not be tolerated.
“Such behaviour is completely unacceptable and runs counter to the values of the game and everything we stand for as a club. There is no room for racism.
“We stand unequivocally with Wes. He has our full support, as do all our players who are too often forced to endure this hatred simply for doing their job.
“We will work with the relevant authorities and platforms in identifying the perpetrators and take the strongest possible action.”
Burnley had to release a similar statement after midfielder Hannibal Mejbri was also racially abused.