The move came after San Luis and Guadalajara, Mexico's two clubs still alive in the Libertadores Cup, withdrew from the South American club championship because Uruguay's Nacional and Brazil's Sao Paulo, scheduled to face San Luis and Guadalajara, respectively, refused to travel to Mexico for their round-of-16 games.
The matches had been postponed a week, but Nacional and Sao Paulo refused to travel to Mexico despite the fact that fears lessened as it became clear that the flu strain was causing relatively mild illness.
Three South American countries had earlier refused to host the series.
"As of today," Decio de Maria, secretary general of the FMF, said, "Mexico is withdrawing from the Copa Libertadores, the Copa Sudamericana and the Copa America."
If relations aren't repaired, the move puts in jeopardy the future of the InterLiga, the SUM tournament that serves as Libertadores Cup qualifying for Mexican cubs.
Necaxa lost out to Tigres of Monterrey in the relegation fight. Necaxa for many years played in Mexico City before moving to Aguacalientes. Like Club America, Necaxa is affiliated with Televisa, Mexico's TV giant.