The aircraft exploded shortly after touching down, leaving two officers stuck inside the burning wreckage.
After the crash, a new gunbattle ensued between the gangs and over 100 policemen, who were backed by Special Police Operations Battalion (BOPE) troops and an armoured vehicle.
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.
Urban violence is widespread in Rio, where nearly one-third of the two-million-strong population lives in favelas.
Rio's win to host the 2016 Olympic Games, the first ever to be held in South America, is a serious challenge for the city in terms of security.
Some 6,000 people were murdered here in 2008 alone.