Videos shared online show flames and smoke at the site in Tehran, and gunshots and explosions can be heard.
An official quoted by state media said the situation was under control, but video footage appeared to show the fire continuing after this.
Iran has been gripped for weeks by anti-government protests.
They first erupted last month after the death of 22-year-old Kurdish Iranian Mahsa Amini in police custody. Officials said she died of a heart attack, but her family disputed this, saying she was beaten by morality police.
BBC Persian’s Rana Rahimpour said it is not yet known whether the situation at the prison is linked to the recent demonstrations.
But this could easily be the case, Rana said, as hundreds of the protesters have been sent to Evin.
State media has suggested the two are not linked, quoting an official who blamed “criminal elements” for the fire.
In a video posted on social media by anti-government monitoring group 1500tasvir, chants of “death to the dictator” – one of the main slogans of the anti-government protest movement – could be heard coming from outside the prison.
Another video appears to show objects being fired into the prison from outside its perimeter, and an explosion is then heard, according to BBC Persian.
Iranian media, which is strictly controlled by the government, reported that the riot started with financial and criminal prisoners, and that no political prisoners were involved. Eight people had been injured, it said.
Speaking from inside the prison, Tehran’s governor told state TV that the riot was in a wing of the prison housing petty criminals and the situation was now completely calm.
However, the situation at the prison is still confused, reports BBC Persian’s Kasra Naji. Videos continue to be posted on social media showing the fire still burning and the sound of gunfire heard around the prison.
Other pictures show inmates on the roof of a section of the prison where political prisoners and many of the protestors who have been arrested in the past four weeks are kept, Kasra said.
The families of some prisoners told the BBC that they were unable to contact their relatives on the phone, which they would normally be able to do, and that internet connection around the prison appeared to have been cut off.
The streets leading to the prison were closed.
Earlier, videos showed riot police entering Evin. There were also reports that special forces had been deployed to the area. A witness told Reuters news agency that ambulances were also there.
British-Iranian dual nationals Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori were both held at Evin prison for several years on spying charges, which they denied, before their release earlier this year.
The prison has long been criticised by Western rights groups. 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.
A group of hackers calling themselves Edalat-e Ali (Ali’s Justice) posted videos in August last year of leaked surveillance footage from Evin prison showing guards beating or mistreating inmates.
Some foreign governments whose citizens are being held in the prison have expressed concern.
A spokesperson for the US state department said it was following events with “urgency”, while the UK Government’s security minister called it a “very worrying development”.
Since the death of Ms Amini five weeks ago, a wave of protests has swept across Iran in the boldest challenge to the Islamic Republic since its establishment in 1979.