The Court of Arbitration for Sport (CAS) ruled that the chant was insulting rather than discriminatory and replaced the fines with a warning.
The FMF was fined 20,000 Swiss francs (15,269.55 pounds) over chanting during the World Cup qualifier against El Salvador in November 2015 and 15,000 Swiss francs (11,452.17 pounds) for the same offence away to Canada the following March.
FIFA said the chant, featuring the Spanish word for male prostitute and usually heard when the opposing team's goalkeeper is taking a goal kick, was discriminatory. But CAS disagreed.
CAS said that "the intention of the Mexican fans....was not to offend or discriminate any specific person" but added that
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the chant "could still be considered discriminatory or insulting in nature and should not be tolerated in football stadiums".
It said that FIFA's reactions to previous incidents may have led the FMF to believe that the chants were not against the rules.
CAS said it had therefore downgraded the fines to a warning but suggested that "in the event similar infringements occur again in the future, harsher sanctions should be imposed on the FMF."
FIFA did not immediately respond to an emailed request for comment.
The chant was widely heard at Mexico games in the 2014 World Cup in Brazil, when FIFA took no action, but the world soccer body has since launched a clampdown and other Latin American teams, including Argentina and Chile, have also been fined.
(Writing by Brian Homewood; editing by John Stonestreet)
