The charges against Cienfuegos Zepeda have not been disclosed and the US authorities have not yet confirmed his detention.
CNN spoke to a US Drug Enforcement Administration spokeswoman who said it could not confirm or deny the detention.
Ebrard added that the Mexican consulate in Los Angeles would inform him of the charges in the next few hours and provide consular assistance to Cienfuegos Zepeda.
Cienfuegos Zepeda was Mexico’s Minister of Defense from 201
CORRECTION: In an earlier version of this story, the name of former Defense Minister General Salvador Cienfuegos Zepeda was misspelled.