The 29-year-old, Leicester's top-scorer last season, was shown a straight red card in the 28th minute by referee Craig Pawson for a two-footed tackle on Mame Diouf.
"Jamie Vardy will serve a three-match suspension with immediate effect after his wrongful dismissal claim was rejected, following an Independent Regulatory Commission hearing," the FA said.
The Premier League champions had earlier on Tuesday said they were appealing for wrongful dismissal.
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"He wants to challenge and get the ball, not make a foul. He touched the ball. Maybe it was yellow," Leicester manager Claudio Ranieri was quoted as saying by the BBC.
Leicester, 15th in the table, host Everton on Dec. 26 and West Ham United on Dec. 31, before visiting Middlesbrough on Jan. 2, with Vardy missing all three matches.
(Reporting by Rex Gowar; Editing by Toby Davis)
