He wrote that Mexico's consul in Los Angeles would be informing him about the charges "in the next few hours", and that Cienfuegos had a right to consular assistance.
The DEA spokeswoman told Reuters she did not have further details on the circumstances of the arrest, whether Cienfuegos was coming or going at the Los Angeles airport, or whether family or others were traveling with him.
The general served from 2012 to 2018 as secretary of defense under President Enrique Pena Nieto.
"We're facing an unprecedented situation" Lopez Obrador added, noting that two former Mexican ministers are now detained in the USA on allegations of links to drug cartels.
The Mexican investigative magazine Proceso, quoting unnamed sources at the US Department of Justice, reported that the arrest was the result of a long-standing US investigation named "Operation Godfather" into corruption involving drug traffickers.
There had been no open probe in Mexico on Cienfuegos and his arrest was linked to the case against Genaro Garcia Luna, Mexico's security minister from 2006-2012, who Lopez Obrador said.
Pena Nieto was in office for six years through December 2018.
"Prosecutors and federal agencies (in the US) always look for information from detainees like Cienfuegos that leads them to people at the same level or above".
Garcia Luna, who served under ex-President Felipe Calderon and was also an architect of the war on drugs, has pleaded not guilty to drug trafficking charges.
U.S. authorities did not warn their Mexican counterparts of the operation. Garcia Luna was arrested in Texas a year ago on suspicion of accepting millions of dollars in bribes from a major drug cartel he was tasked with combating.
While defence minister, Cienfuegos complained about his troops having to take part in the country's war on drug trafficking, saying the military was not suited for the job.
Mexico's attorney general charged three Mexican soldiers with homicide in 2014 in connection with the shooting deaths of 22 suspected gang members in the "Tlatlaya Massacre".
The armed forces have taken an increasingly prominent role in fighting crime in Mexico, and generally are perceived as less prone to corruption than civilian police forces.
Current President Andres Manuel Lopez Obrador has vowed to go after corruption and lawbreaking under past administrations, but he has relied more heavily on the army - and given it more tasks, ranging from building infrastructure projects to distributing medical supplies - than any other president in recent history.