The plane came down during a heavy rainstorm near the airport of Rio Branco in the Amazon state of Acre, witnesses said.
An engine is said to have fallen from the plane about 800 metres (half a mile) from the crash site, but it is not clear if this is what caused the crash, the Associated Press news agency reported.
Heavy rain is common in the afternoon and evenings in the Amazon and flights are often cancelled or re-routed as a result.
Police told Reuters news agency that between 28 and 30 people were on board the plane at the time of the crash.
Rescue hampered
Reports say that several people survived the crash, which happened in thick jungle several kilometres from the runway.
One managed to escape relatively unscathed and called his parents on his mobile phone to tell them of the accident.
Two of the dead were local politicians. One was named as Ildefonco Cordeiro, a federal congressman representing the state of Acre.
Local firefighters are at the crash scene, but inhospitable terrain and a lack of roads are making rescue attempts difficult, the French news agency AFP reported.
"Some bodies were hurled more than 200 metres [650 feet] from where the airplane crashed," one fire official told local news sources.
The aircraft involved, a small, Brazilian-made aircraft called a Brasilia plane, was operated by Rico Airlines, a company that has been flying between cities in the Amazon for more than 50 years.
It had taken off from the city of Cruzeiro do Sul, near Brazil's border with Peru.
Officials have opened an investigation into the cause of the crash, Reuters news agency reported.