The prisoners set fire to blankets and beds in a cell in the Sanliurfa city prison late Saturday, but it was brought under control before it could spread throughout the jail, which holds 1,000 inmates, the Anatolia news agency reported, quoting governor Celalettin Guvenic.
Another five inmates in the cell were hospitalised, it said.
The fire broke out during a fight between inmates, Turkey's Prime Minister Recep Tayyip Erdogan told Anatolia, relaying a survivor's account.
"I was also informed by the governor that the conditions in the cell were not suitable to accommodate that many inmates," he added. Sanliurfa, the city's largest jail, reportedly has a capacity of around 250.
The mutiny may have been in protest at poor conditions and lack of air conditioning, the NTV news channel reported earlier, citing prison sources.
Local media frequently criticise conditions at the jail, which also holds several political prisoners including a lawmaker from the opposition Peace and Democracy Party, security sources told AFP.
The fire broke out in a cell for ordinary prisoners.
Police and gendarmerie were deployed as large crowds gathered outside the jail.
Police blocked road access and resorted to pepper spray to disperse angry families demanding to be informed of the dead prisoners' identities.
Families were allowed to visit their relatives on Sunday after calm was restored in the prison amid panic and protests over the deaths.
An investigation was under way to establish what happened.
In September 2010, a political prisoner set himself on fire in the same prison after he was transferred to the ordinary prisoners' section, triggering protests from other inmates, but no one was killed.