Venezuela's prisons minister said that the incident resulted from an escape attempt and that the Los Llanos prison director had been shot and wounded.
Prisoners fought each other with handguns and knives, which were seized after the fight, said the state's Public Security Ministry.
An NGO quoted local residents as saying explosions and then gunfire were heard starting late Monday, with the violence continuing overnight.
No guns or knives were used in the killings, which prison officials said appeared to have been sparked by a "rift between prisoners who belonged to the same criminal group and were involved in drug trafficking in the state."
The shooting of a 22-year-old black man in the city of Nantes earlier this week had sparked four nights of rioting. The officer initially claimed he acted in self-defence, but later told investigators he had fired his weapon by accident.
Violence erupted during opposition protests which raged overnight into Saturday after the controversial election victory of President Uhuru Kenyatta.
Demands for water, housing, electricity and jobs are at the centre of protests that have rocked areas throughout the country.
Six businesses were destroyed by fire and police cars damaged before calm was restored in the neighborhood. The unrest began several hours after a man fleeing police after a traffic stop was shot and killed.
Several people, including journalists, were wounded when riot police in Harare used batons, tear gas and water cannon to disperse demonstrators protesting against the handling of the economy by President Robert Mugabe's government.
The French Government has reversed its decision to ban a protest against labour reforms in Paris, where police are already stretched thin due to terrorist threats and violence related to the Euro 2016 tournament.
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