Cienfuegos faces four counts for his alleged operation to smuggle heroin, cocaine, methamphetamine and marijuana into the United States from December 2015 to February 2017.
Late on Thursday, Mexican Foreign Minister Marcelo Ebrard said Cienfuegos was detained at the airport in Los Angeles, California.
Media reported that Cienfuegos was arrested by US officials at the request of the US Drug Enforcement Administration.
A defence minister has never been arrested in the history of Mexico, the report said citing former Mexican foreign minister Jorge Castaneda.
Cienfuegos had served as the Mexican defence minister from 2012 to 2018 under former president Enrique Pena Nieto.