Ferretti, who enjoyed a previous stint as interim coach in 2015, was born in Brazil but spent most of his playing career and has done all his coaching in Mexico.
He is not expected to leave his role as coach of Club Tigres, the side he led to the Copa Libertadores final in 2015 and the CONCACAF Champions League in 2016 and 2017.
"Our gratitude and recognition go to professor Ferretti for his disposition and commitment to the Mexican national side," the FMF said in a statement. "We thank Club Tigres for collaborating in this process."
Mexico have been without a coach since Juan Carlos Osorio stood down shortly after leading the side to a last-16 place in the World Cup in Russia.
Mexico play Uruguay in Houston on Sept. 7 and face the U.S. in Nashville four days later.
(Reporting by Andrew Downie, editing by Ed Osmond)
