An airport official said the plane, carrying 18 passengers and crew, slammed into waters near an airport at the coastal town of Sarmi in fine weather just before its scheduled landing on Tuesday.
Airport official Bela Hafni said three people survived but are in critical condition.
"Five minutes before it was expected to land, the pilot contacted us. Suddenly, within seconds, the plane fell 500m before the runway," Hafni said from Sarmi, 3600km east of Jakarta.
"When the pilot contacted us, he reported there was an engine problem," Hafni said, adding the pilot was among the dead.
Police among dead
The survivors have been transported to the Papua provincial capital Jayapura. The wreckage of the plane now lies in pieces near the shore off Sarmi.
"Five minutes before it was expected to land, the pilot contacted us. Suddenly, within seconds, the plane fell 500m before the runway"
Sarmi airport official
Several of the dead passengers were police officers, a police spokesman said.
There are periodic plane crashes in Indonesia, the world's largest archipelago, where bad weather and rough terrain can create hazardous conditions, especially for light planes.
Indonesia's worst air disaster occurred in 1997 when a Garuda Indonesia Airbus A300-B4 crashed in a mountainous area on the island of Sumatra in poor visibility, killing all 234 people on board.