Gonzalez said the inmates had firearms and that police are investigating who smuggled the weapons into the prison.
Manuel del Castillo, a Ciudad Juarez spokesman, initially said the inmates had taken the firearms from prison guards but Gonzalez said that isn't clear.
He said a woman who was being tried for homicide and kidnapping was among those killed and that four other prisoners were badly wounded.
Soldiers and federal and state police officers took control of the prison early Tuesday, Gonzalez said.
Mexican cartels are fighting for control of Ciudad Juarez, which sits across the border from El Paso, Texas. More than 6,000 people have been killed in drug-related violence in Juarez over the past two years.
