The incident, which took place in the city’s Jacarezinho neighborhood, is reportedly the deadliest single police operation in the state.
Suspects had tried to escape across rooftops as police tailing them in vehicles entered the province.
Several bullets were fired during the chase, hitting two passengers on a nearby metro train.
Three policemen were also hit and one died of his wounds.
Among the dead were some of the leaders of the drug trafficking ring that dominated life in the area.
In a statement on its Facebook page, Civil Police in the city said it was “with extreme regret” that police inspector Andre Leonardo de Mello had been killed “during the operation to combat organised crime in the community of Jacarezinho.
The chase was based on concrete intelligence and investigation information, it added.
“Unfortunately, the war scenario imposed by these gangs demonstrates the importance of operations so that criminal organizations do not strengthen themselves.
“Sepol solidarity with friends and family, and feels very much the pain for the death of the inspector who had a clear trajectory in the institution, being admired and respected by all.
“He honoured the profession he loved and will be missed. But it also leaves the feeling that work can’t stop,” the Civil Police added.
The civil force said its Secretariat also “regrets the innocent victims hit on the subway.”
At least 10 suspects have been arrested.
“This is the largest number of deaths in a police operation in Rio, surpassing 19 at Complexo do Alemão slum in 2007, except we did not lose one of ours in that action,” police chief Ronaldo Oliveira told Reuters.