The match had been overshadowed by accusations that referee Mark Clattenburg had racially abused the Chelsea midfielder.
But Clattenburg was later cleared of all charges.
Mikel had admitted using threatening and/or abusive and/or insulting words and/or behaviour in the official's changing room at the end of the game at Stamford Bridge on October 28, said the Football Association.
"Chelsea's John Obi Mikel has been given a three-match suspension to begin with immediate effect and fined ?60,000 following an Independent Regulatory Commission hearing today," said an FA statement.
"The Regulatory Commission's independent chairman Christopher Quinlan QC emphasised that the Independent Regulatory Commission accepted, as did The FA, that at the time he threatened the referee the player genuinely believed that the referee had racially abused him.
"But for that factor the suspension would have been significantly longer. Subsequently The FA investigated the allegation that the referee racially abused the player and found that there was not a case for him to answer."