The Spaniard was punished for his reaction after his dismissal at Everton in an FA Cup tie last month.
The 27-year old clashed with Everton midfielder, Gareth Barry and appeared to bite the Englishman, however, the later claimed no contact was made.
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Costa was then handed his first red card of his Chelsea career by referee Michael Oliver, he then protested angrily and delayed leaving the pitch.
He was originally handed a two-match ban, but will now miss three games
An FA statement read: “Chelsea’s Diego Costa has been given a one-match suspension, fined £20,000 and warned as to his future conduct.
“The forward admitted a charge of improper conduct in relation to his behavior after he was shown a second yellow card in The FA Cup Sixth Round tie on 12 March 2016 at Goodison Park.
“This suspension will follow immediately on the conclusion of the player’s current ban.”
A further one-match ban means he will miss Chelsea’s trip to Swansea as well as Saturday’s clash against Aston Villa, after missing the 2-2 draw against West Ham on 19 March.