A police source told TASS, the Russian state news agency, that IS members who were due to appear in court on terrorism charges were among the hostage-takers.
They were reported to have been holed up in the prison courtyard, armed with a pocket knife, a baton and an axe, the source said.
The Interfax news agency reported that there were six hostage-takers, who demanded to be provided with a car and to be allowed to leave the prison in exchange for the release of the hostages.
The incident comes nearly three months after gunmen killed at least 144 people when they opened fire inside a concert hall near Moscow in an attack claimed by the jihadist group.
Hundreds more were injured in the March 22 attack at the Crocus City Hall, the deadliest on Russian soil for two decades.
More than 20 people have since been arrested, including the four suspected gunmen. All are from the former Soviet republic of Tajikistan, an impoverished country on Afghanistan’s northern border.
Russia has been repeatedly targeted by attacks claimed by IS militants, though the jihadist group’s influence in the country remains limited.
Russian media reports speculated that the attackers at the Rostov detention centre could be among those arrested in 2022 for allegedly planning an attack on the Supreme Court of Karachay-Cherkessia, a Muslim-majority Russian republic in the Caucasus.
Nearly 4,500 Russians, mainly from the Caucasus, travelled to Iraq and Syria to fight with Islamic State, according to official figures.
In April, two armed men who authorities said were members of “an international terrorist organisation” were shot dead by Russian forces near Nalchik in the Caucasus.
