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Mikel had already admitted a charge that he confronted referee Mark Clattenburg in the official's changing room after the game.
Thursday's decision by the Independent Regulatory Commission revealed the sanction, which included a £60,000 fine, would have been "significantly longer" but for the fact Mikel had believed he had been racially abused by Clattenburg.
The suspension will take effect immediately and rule Mikel out of domestic duty until Boxing Day.
"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 [Thursday 6 December 2012]," an FA statement read.
"Mikel had requested a personal hearing after admitting an FA charge of using threatening and/or abusive and/or insulting words and/or behavior.
"The breach of FA Rule E3 was in relation to an incident which occurred in the match official's changing room at the end of Chelsea's fixture against Manchester United on 28 October 2012.
"The Regulatory Commission's independent chairman Christopher Quinlan QC emphasized 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."
Mikel, who signed a new five-year deal on Wednesday, will therefore miss the weekend's trip to Sunderland but will be available when Chelsea jet out for the Club World Cup in Japan next week.
His availability when the Blues return from the Far East could be limited, though, with the midfielder due to meet up with Nigeria early in the new year for the African Nations Cup.
That tournament begins on January 19, with the players set to convene in the weeks beforehand, and Mikel would be unavailable until February 10 should Nigeria reach the final.
New boss Rafael Benitez appeared to begin preparations for his absence last night when he employed David Luiz in midfield at stages of the 6-1 Champions League win over FC Nordsjaelland.
Benitez admitted after the match he was prepared to use Luiz further up the pitch and provide support for holding midfielders Ramires and Oriol Romeu, who both started Wednesday night's game.
The Associated Press was used in this report.