The fire broke out late Sunday in one of the cellblock complexes of a maximum security prison for men in the central province of Santiago del Estero, said Ricardo Daives, the province's justice minister.
Another 10 people were hospitalized for smoke inhalation and other injuries, Daives told the independent news channel Todo Noticias.
Daives said inmates apparently set the fire in a bid to distract guards as part of plan to break out of the prison.
"Parts of the cellblock 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," Daives added.
Prison officials said none of the inmates managed to escape.
Riot police fired rubber bullets and tear gas to restore calm after about 200 relatives, some throwing rocks, tried to break through barricades blocking the entrance to the penitentiary, 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 Santiago de Estero, the provincial 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 Oct. 16, 2005 , at a penitentiary in Magdalena , southeast 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.