The Boeing 737, operated by Merpati Nusantara Airline, was landing at Manokwari airport when it slid into a small canal at the end of the runway, police official Didi Zaenal said. He said the plane flew in from the nearby city of Sorong.
About 20 passengers, most with bruises and some with broken bones, were taken to a local hospital for treatment, paramedics and hospital officials said. There were no reports of fatalities.
Local police chief Bambang Ricky told Indonesia's official Antara news agency that the plane's fuselage was split open in the accident. He said there were 103 passengers and six crew on board.
Papua, about 1,830 miles east of the capital, Jakarta, is one of the most isolated and underdeveloped regions of Indonesia.
There are few roads in the province, which occupies the western half of the island of New Guinea, and air travel is a common form of transport.
Indonesia has seen a string of air crashes in recent years.