The Argentine, who led Mexico to the last 16 at the World Cup in Germany and was third-choice goalkeeper in his own country's World Cup winning squad in 1978, had been in his latest job for almost exactly a year.
"The professional relationship between the club and Ricardo Antonio La Volpe has ended because of some financial differences," said the club in a statement.
The famously grumpy La Volpe, who stands out on the touchline by wearing brightly-coloured ties featuring Chinese dragons, is one of Latin America's most controversial and outspoken coaches.
During his four years in charge of Mexico, he was involved in a continual slanging-match with former striker Hugo Sanchez and caused a storm by leaving Cuauhtemoc Blanco, the country's most naturally gifted player, out of the World Cup squad.
Last year, he stoked the rivalry with Monterrey's arch-rivals Tigres UANL, as he dubbed them boring and said before a derby that he would rather take up baseball or go shopping than watch them play.
