The world football body gave no details of the nature of the insults, but media reports said Mexican fans aimed the shouts at Germany goalkeeper Manuel Neuer at Moscow’s Luzhniki Stadium.
Mexico inflicted a shock 1-0 defeat on the World Cup holders in the match on Sunday.
Fifa took no action when the same chant was widely heard during Mexico’s game against Brazil in the 2014 World Cup.
It now takes a harder line, and other Latin American teams have been fined for the same chant.
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