Four prisoners died in a fire that raged overnight in the Iranian capital's notorious Evin prison, according to the judiciary in a country that has been rocked by a month-long protest movement sparked by the death of a young woman in custody.

"Four prisoners died due to smoke inhalation caused by the fire and 61 were injured," the judicial authority's website Mizan Online reported, adding that four of the injured were in "serious condition".

Rights groups had voiced grave fears for the inmates after gunshots and explosions were heard during the blaze from inside the complex.

The fire – blamed on "riots and clashes" and later brought under control according to authorities – came as Iran has been rocked by protests over the death of 22-year-old Mahsa Amini after her arrest for violating Iran's strict dress code for women.

The demonstrations have turned into a major anti-government movement in the Islamic republic, giving the clerical leadership with one of its biggest challenges since the ousting of the shah in 1979.

Evin, infamous for the ill-treatment of political prisoners, also holds foreign detainees and thousands facing criminal charges. Hundreds of those arrested during the recent demonstrations have reportedly been sent there.

"The life of every political and ordinary crime prisoner (in Evin) is at grave risk", the Oslo-based non-government group Iran Human Rights (IHR) warned overnight.

It said authorities had closed off roads leading to the prison in an apparent bid to stop protests taking place outside the jail.

But some headed there on foot and chants of "Death to the dictator" could be heard in videos shared by social media channel 1500tasvir.

"Prisoners, including political prisoners, are completely defenceless inside that prison," said Hadi Ghaemi of the New York-based Center for Human Rights in Iran (CHRI).

Freedom of expression group Article 19 said it had heard reports of telephone and Internet connections at Evin being cut.

Iranian rights activist Atena Daemi, herself a long-time inmate of Evin, wrote on Twitter that in the early hours of Sunday several buses and ambulances were seen leaving the prison. (AFP)