President Joseph Kabila refused to quit office in line with the constitution at the end of his second elected five-year term.
"For about an hour, there's been shooting around the Makala prison, there's no more traffic and the avenues are empty here in Selembao," the poor city centre district where the prison stands, Emmanuel Cole, a prisoners' rights activist, said.
"There's shooting with light weapons... the market is closed," resident Philemon Mboko told AFP, adding that a police chief "has been killed".
"I took shelter inside the house. I heard a lot of gunfire next to the Makala prison," another resident, Fiston, said.
"Something is happening in the Selembao area. We are trying to find out exactly what is going on," police spokesman Colonel Pierrot-Rombaut Mwanamputu, told AFP.
Between May and July, a number of attacks and jailbreaks hit the Makala prison, the biggest in Kinshasa, capital of the vast Democratic Republic of Congo.
More than 4,000 detainees were able to escape during those incidents.
Police stations in three Kinshasa districts -- Limete, Matete and Kalamu -- also came under attack, along with the central market, whose chief administrator was targeted and killed.
Police have identified some of the alleged perpetrators as members of the main opposition Union for Democracy and Social Progress party, long led by Etienne Tshisekedi, who died last February aged 84.
Insecurity has deepened in the DRC since December, when President Joseph Kabila refused to quit office in line with the constitution at the end of his second elected five-year term.