The shoot-out took place during a police operation in a favela in the Jacarezinho area of the city.
Police launched the operation after receiving reports that drug traffickers were recruiting children for their gang.
Two passengers on a metro train were hit by bullets but survived.
Police in the Brazilian city confirmed the death of one of their officers, Inspector Andre Leonardo de Mello Frias. A statement on Facebook said "he honoured the profession he loved and will be missed".
