The helicopter had been carrying six police officers as part of an operation in Morro dos Macacos, one of Rio's hundreds of slums, which is dominated by heavily armed drug gangs, police said.
Police were responding to gun fire between rival drug gangs nearby before the incident happened shortly after dawn.
After the crash, a fresh gun battle broke out as more than one hundred policemen backed by armoured vehicles and special forces tried to regain control of the area.
Urban violence is widespread in Rio, where nearly one-third of the two-million-strong population lives in favelas.
The incident comes just weeks after the city was awarded the 2016 summer Olympics.