The prosecutors' office said an investigation had been launched into "the deaths of 37 people" in the facility in the town of Puerto Ayacucho.
Governor Liborio Guarulla had earlier tweeted that a "massacre" took place with at least 35 corpses counted.
Prosecutors said 14 officials were wounded in the violence, but did not say if any were among the dead.
Two prison-monitoring groups, A Window to Freedom and the Venezuelan Prisons Observatory, said the 37 killed were all inmates.
"This is the worst riot we've had in a detention facility," Carlos Nieto of A Window to Freedom told AFP.
"In this one, detainees are only supposed to be held for up to 48 hours, but there were prisoners who have been there for years," he said.
The jail was holding 105 prisoners at the time of the riot, Guarulla said.
It comes as Venezuelan President Nicolas Maduro paid tribute to the late leftist icon Fidel Castro during a surprise visit to Cuba, state media reported Wednesday.
The daily Granma said Maduro traveled Tuesday to Castro's tomb in Santiago de Cuba.
Maduro was accompanied by his wife Cilia Flores, Cuban President Raul Castro -- Fidel's brother -- and Cuban Foreign Minister Bruno Rodriguez, according to the newspaper.
"On the 91th birthday of the Commander in Chief a tribute by the president of Venezuela was appropriate for someone who always stood by the Bolivarian revolution," the newspaper said.
Fidel Castro, born on August 13, 1926, died in November 2016. His remains are buried at the Santa Ifigenia cemetery in Santiago de Cuba, some 960 kilometers east of Havana.
Venezuela is Cuba's most important economic and political ally, and Havana has offered strong support for Maduro's embattled leftist regime.
UN calls for solution to crisis
UN Secretary General Antonio Guterres urged the Venezuelan government and opposition on Wednesday to re-start negotiations, calling for a brokered solution to the country's economic and political crisis.
Venezuelan President Nicolas Maduro has ordered the army to conduct a round of military drills later this month in response to US President Donald Trump's threat of military action in the crisis-stricken nation.
The oil-exporting South American country has been plunged into economic chaos and rocked by angry street protests from opponents demanding Maduro's removal. Nearly 130 people have died in recent months of unrest.
"Venezuela needs a political solution based on dialogue and compromise between the government and the opposition," Guterres told reporters at UN headquarters, backing international and regional efforts to advance talks.
"I strongly support those efforts. I've been in close contact with all of them, and I urge the government and the opposition to restart negotiations because I believe that only solution is a political solution."
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US rallies LatAm on Venezuela after Trump military warning
Trump said last week that he was considering a range of scenarios for Venezuela and was "not going to rule out a military option." Russia on Wednesday called any threats against Venezuela "unacceptable."
Trump's apparent threat was also roundly condemned across Latin America, even by states opposed to the socialist Maduro.
"Latin America has successfully managed to get rid of both foreign intervention and authoritarianism, and this is a lesson that is very important to make sure that this legacy is safeguarded," said Guterres.
