The Frenchman, who made a "quenelle" salute after scoring in a 3-3 draw against West Ham United on December 28, has also been ordered to complete a compulsory education course.
"An Independent Regulatory Commission has found an aggravated breach of FA Rule E3 against Nicolas Anelka proven and has issued a five-match suspension and a fine of £80,000, pending appeal," the FA said in a statement.
The punishment is suspended until the outcome of any appeal or until the player informs the FA of his decision not to appeal.
Anelka had previously used his Facebook and Twitter accounts to ask the FA to drop the charges and denied he was anti-Semitic or racist.
He had claimed the gesture, which has been described as an inverted Nazi salute, was a tribute to his French comedian friend Dieudonne M'Bala M'Bala who invented it.
Image: Nicolas Anelka
Photograph: Christopher Lee/Getty Images
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