Four inmates who was detained for robbery, died of smoke inhalation. On Sunday, the Iranian the judiciary said 61 people were injured, including 10 who needed hospital treatment with four in a serious condition.
Iranian state media reported that the fire was put out after several hours, with no prisoners managing to escape despite a series of failed attempts.
Gunshots were also heard at the prison as plumes of smoke rose from the building with alarms going off, according to local media and online videos.
Elvin prison houses hundreds of inmates, including a large number of political prisoners with charities reporting repeated human rights abuses.
The US-based Center for Human Rights in Iran claimed that an “armed conflict” had broken out at the prison.
They added that gunshots were initially heard in Ward Seven of the prison.
Video footage from the activist website 1500tasvir appeared to suggest that special forces on motorbikes were heading towards the prison.
It comes as anti-government protests in Iran continue into their fifth week in response to the death of Mahsa Amini last month.
Ms Anmini, 22, died after being arrested by Iran’s “morality police”, who often police the dress of women in public.
“Iran has turned into a big prison,” videos on social media showed university students in Tehran chanting.
They also shouted: “Evin prison has become a slaughterhouse.”
Other videos showed fires lit at intersections in several cities, including Tehran and Piranshahr, where drivers honked their horns and anti-government slogans could be heard.
On Sunday, Iran’s president, Ebrahim Raisi, accused his US counterpart Joe Biden of inciting “chaos, terror and destruction”.
He said: “The American president, who allows himself through his comments to incite chaos, terror and destruction in another country, should be reminded of the eternal words of the founder of the Islamic Republic, who called America the Great Satan.”
On Saturday, Biden called on Iran to “stop the violence against its own citizens by simply exercising their basic rights”.