Guerrero state prosecutors say in a statement the three men died yesterday but released few other details.
Spokesman Jose Villanueva says investigators are waiting for autopsy results to determine a cause of death.
Prosecutors say the inmates had been sentenced to at least eight years in prison for robbery and homicide.
They had been transferred to Acapulco from a prison in Iguala, where five gunmen and four inmates died in a shootout last week.
Authorities said a group of gunmen managed to enter the facility and opened fire, killing the inmates. Guards killed the gunmen.