Charges against Cienfuegos Zepeda have not been announced, and US authorities have not yet confirmed his detention.
A US Drug Enforcement Administration spokeswoman would not confirm or deny the detention.
“It is a very regrettable fact that a former defense secretary is detained, accused of drug trafficking,” Mexico’s President Andrés Manuel López Obrador, commonly known as AMLO, said during his daily press briefing on Friday.
Cienfuegos Zepeda was Mexico’s defense minister from 2012 to 2018. He served under President Enrique Peña Nieto, who left office two years ago.
Ebrard said the Mexican Consulate in Los Angeles would inform him of the charges against Cienfuegos Zepeda and provide consular assistance to him.
Mexico’s president said the general was to appear in a US federal court later Friday.
AMLO defended the armed forces, calling them “incorruptible” and “pillars of the Mexican state” while blaming former administrations of what he called the “neoliberal period” when tens of thousands of Mexicans were killed in drug-related violence and cartel warfare.
CORRECTION: An earlier version of this story misspelled the name of the former defense minister General Salvador Cienfuegos Zepeda.