There was no immediate confirmation of the cause of death.
Armendáriz made his debut on the big screen in 1966 and in a career that spanned over 200 films and television credits, he was best known for playing sly, sometimes cynical characters he endowed with wit and charisma.
Armendáriz played Gov. Riley in the 2005 movie "The Legend of Zoro," and had roles in 1989's "Old Gringo" and "Once Upon a Time in Mexico" in 2003.
President Felipe Calderón's office issued a statement lamenting Armendáriz' death, calling him "a great actor who reflected well on Mexico at home and abroad."
The Mexican government news agency Notimex reported he died in New York City of cancer, but said his family had asked for their privacy to be respected.
He acted in more than 100 films, including the Mexican hit "The Crime of Father Amaro."
Consuelo Sáizar, the president of Mexico's National Arts Council, lamented the death of Armendáriz in her twitter account.
He had been married and divorced twice and is survived by several children.
Armendáriz' father bore the same name and was a movie star during the "golden age" of Mexican films in the 1940s and 50s.
Based on reporting by the Asssociated Press.