Police said the Avia Star plane was transporting cargo from the provincial capital, Jayapura, to the nearby district of Wamena when it went down.
Major General Bagus Ekodanto said the bodies of the pilot, co-pilot and two other crew members had been pulled from the smouldering wreckage.
The crash occurred at about 0700 (2300 GMT on Wednesday) on Pike Mountain.
The cause of the crash remains unclear, although the local terrain is mountainous, often wreathed in low clouds, and the weather changeable and dramatic.
The Antara state news agency quoted a witness who claimed to have seen the plane circling around a hill before tumbling from the sky.
There are few roads in Papua, which occupies the western half of New Guinea, and air travel is a common but frequently risky form of transport.