Suspects tried to escape across rooftops as police entered the slum in armoured vehicles and helicopters flew overhead, television images showed.
Bullets fired during the shootout struck a light rail coach, wounding two passengers, the fire brigade said.
Three policemen were hit and one died of his wounds, police said.
It was the deadliest single police operation in the state of Rio de Janeiro, which has suffered for decades from drug violence in its poor neighbourhoods known as favelas.
"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.
Police said that among the dead in Jacarezinho were leaders of the drug trafficking gang that dominated life in the slum. At least 10 suspects were arrested, they said.