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.
He said that his grandmother could have played for the United States after Mexico lost to them in a World Cup qualifier in 2005 and argued with FIFA officials when he was banned from smoking on the touchline during the Confederations Cup.
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.
Not for the first time, his comments back-fired as Tigres won the derby 4-1 and La Volpe was sent off for protesting.
