"Parts of the cell-block were set on fire and that produced this whole situation," he said.
The minister said mattresses and other flammable materials inside one of the seven prison units swiftly caught fire, spewing dense smoke.
The entire prison houses more than 475 inmates but Daives said other pavilions were not affected.
"Autopsies will be conducted and the bodies handed over to the families in the coming hours," he said.
Prison officials said none of the inmates managed to escape.
Riot police fired rubber bullets and tear gas to restore order after about 200 relatives, some throwing rocks, tried to break through barricades blocking the entrance to the building, the government news agency Telam reported.
Broadcast television news footage showed relatives hugging each other and then trying to tear down anti-riot barricades manned by police outside the prison in the city of Santiago de Estero, capital of the province of the same name.
Firefighters could be seen pouring water on the flames amid a scene of drifting smoke and wailing ambulances arriving and leaving.
The last major prison fire in Argentina killed 32 inmates on October 16, 2005, at a penal unit in Magdalena, south-east of the Argentine capital of Buenos Aires.
The worst prison tragedy in Argentina's modern history was the Villa Devoto uprising in March 1978 in the capital in which 61 people died.