Football's world governing body stated that the Mexico case involved "discriminatory and insulting chants" during the team's 1-0 victory over World Cup holders Germany on Sunday.
Mexican fans chanted an anti-gay slur when Germany goalkeeper Manuel Neuer prepared to kick the ball clear. The chant - "puto", the Spanish word for a male sex worker - is a common insult among Latin American football crowds and has led to Fifa fining several federations at World Cup qualifying games.
Fifa says it noted the FMF's effort to persuade fans to stop the chants. The federation was warned, and faces extra sanctions for similar incidents in Russia.
The FMF was sanctioned 12 times for homophobic chanting during the World Cup qualifying campaign, receiving warnings for the first two offences and fines for 10 more.
Mexico striker Javier Hernandez posted a message on Instagram on Wednesday asking fans to end the derogatory chant that is usually shouted during their opponents' goal kicks.
"To all Mexican fans in the stadiums, don't shout 'Puto'," Hernandez said. "Let's not risk another sanction."
Although the Mexican team has appealed before for an end to the chants - the players even released a video on the subject in 2016 - some supporters have not relented.
The chant was widely heard at Mexico games in the 2014 World Cup in Brazil, when Fifa took no action, but the governing body has since launched a clamp-down. Other Latin American teams, including Argentina and Chile, have also been fined.
Fifa is employing three specialist observers at each World Cup match to report discriminatory behaviour by spectators.
The football association of Serbia (Sff) has also been fined the same amount following a case involving an "offensive and political" World War II-era banner at the team's 1-0 win over Costa Rica. Serbia has had problems with far-right nationalist fans in the past.
Additional reporting by Reuters and the Associated Press.