State news agency IRNA on Saturday said eight people were injured in the unrest, which erupted after nearly a month of protests across Iran over the death in detention of Mahsa Amini, a 22-year-old Kurdish Iranian woman.
The protests have posed one of the most serious challenges to the Islamic Republic since the 1979 revolution, with demonstrations spreading across the country and some people chanting for the death of Supreme Leader Ayatollah Ali Khamenei.
An Iranian judiciary statement said a prison workshop was set on fire "after a fight among a number of prisoners convicted of financial crimes and theft".
Tehran's fire department told state media the cause of the incident was under investigation.
The prison, located in the foothills at the northern edge of the Iranian capital, holds criminal convicts as well as political detainees.
A security official said calm had been restored at the prison, but a witness said ambulance sirens could be heard and smoke still rose over the prison.
"People from nearby buildings are chanting 'Death to Khamenei' from their windows," the witness said.
The prison mostly holds detainees facing security charges, including Iranians with dual nationality. It has long been criticised by Western rights groups and was blacklisted by the US government in 2018 for "serious human rights abuses".
US State Department Spokesman Ned Price tweeted, "We are following reports from Evin Prison with urgency. We are in contact with the Swiss as our protecting power. Iran is fully responsible for the safety of our wrongfully detained citizens, who should be released immediately."
Human Rights Watch has accused authorities at the prison of using threats of torture and of indefinite imprisonment, as well as lengthy interrogations and denial of medical care for detainees.
"No security (political) prisoner was involved in today's clash between prisoners, and basically the ward for security prisoners is separate and far from the wards for thieves and those convicted of financial crimes," an unnamed official told the Tasnim news agency.
The unrest at Evin prison occurred after nearly a month of protests across Iran since Amini - a 22-year-old woman from the country's Kurdish region - died on September 16 while being held for "inappropriate attire".
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