Murray was dismissed during Brighton's 2-1 Championship win against Sheffield Wednesday for handling a Glenn Loovens shot, with the score 1-1.
The resulting penalty was saved by David Stockdale and Albion went on to win through a late Anthony Knockaert strike.
Albion appealed against the decision as they felt keeper Stockdale was behind Murray and would have saved the shot, while Murray was also looking to protect his face.
However, the FA Independent Regulatory Commission have rejected the club's appeal and top-scorer Murray will now miss tomorrow's home game with Cardiff City.
In a tweet, the FA said: "Glenn Murray will serve a one-match suspension after his wrongful dismissal claim was rejected by an Independent Regulatory Commission.
"The #BHAFC forward was sent off for denying an obvious goalscoring opportunity during the game against #SWFC on 20 Jan 2017."
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