Ebrard said he was informed of the detention by US Ambassador to Mexico, Christopher Landau.
Charges against Cienfugos Zepeda have not been announced, and US authorities have not yet confirmed his detention.
CNN spoke to a US Drug Enforcement Administration spokeswoman, who said they 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 Cienfugos Zepeda.
Cienfugos Zepeda served as Mexico's defense minister from 2012 to 2018, under President Enrique Peña Nieto.
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