The office said the case showed a “pattern of irresponsibility.”
The head of the agency, Francisco Garduño, could not be immediately contacted for comment.
Prosecutors said another official would also face charges, but did specify exactly what they were.
Also Tuesday, Mexico’s president said two guards seen fleeing when the fire broke out did not have keys to the cell door. The blaze at the facility in the border city of Ciudad Juarez shocked the country.
The comments by President Andrés Manuel López Obrador came on the same day that the bodies of 17 Guatemala migrants and six Hondurans killed in the fire were flown back to their home countries.
It was unclear what effect López Obrador’s comments might have on the trial of the guards.
“The door was closed, because the person who had the keys wasn’t there,” López Obrador said.
A video from a security camera inside the facility shows guards walking away when the fire started in late March inside the cell holding migrants.
The guards are seen hurrying away as smoke fills the facility, and they did not appear to make any effort to release the migrants.
Three Mexican immigration officials, a guard and a Venezuelan migrant are being held for investigation in connection with the fire. They face homicide charges.
The migrant allegedly set fire to foam mattresses at the detention center to protest what he apparently thought were plans to move or deport the migrants.
In Guatemal City, relatives of the victims gathered at an air force base with flowers and photos of the deceased to mark their return.
“My son, my love,” a female voice could be heard calling out, amid sobs from those present as the coffins were unloaded and placed in a line, and relatives were allowed to approach them.
Mexican military planes carried the bodies six migrants to Honduras and 17 to Guatemala. Authorities say 19 of the 40 dead were from Guatemala, but two bodies were still in the process of having their identities confirmed.
An additional 11 Guatemalans were injured in the fire.
Guatemalan Foreign Minister Mario Búcaro accompanied the bodies, which were to be taken overland to their hometowns in nine different provinces.
Some bodies of Salvadoran migrants were returned to El Salvador last week. So far, 31 bodies have been sent back to their home countries.