FIFA said on Tuesday it had warned the FMF about the misconduct of a "small group of Mexican fans in relation to insulting and discriminatory chants" during Sunday's 2-2 draw against Portugal.
Mexico fans have long shouted an insult at keepers taking goal kicks which gay rights groups argue is homophobic.
Mexican media said the chant was heard again on Sunday when Portugal goalkeeper Rui Patricio took goal kicks, though on a smaller scale than in the past.
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"As you know, FIFA is very serious about the chanting that we do when the goalkeeper takes a kick, and the possible sanctions are serious," FMF said in a statement directed at the team's supporters.
"Our efforts on the pitch will come to nothing if, because of this (behaviour), we lose the match, the game is suspended or you are expelled from the stadium.
"We lose, you lose, everyone loses."
Mexico have already been fined eight times during the course of the World Cup qualifying competition because of homophobic chanting.
The matches in question were at home and away to El Salvador, home and away to Canada, at home to Honduras, away to the United States, and at home to Panama and Costa Rica in a period starting in November 2015 until this March.
Mexican media said the chant was also heard at matches at home to Honduras and the U.S. earlier this month, although FIFA could not immediately reached for comment on whether disciplinary proceedings had been opened in those cases.
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