RNZ reports the Hercules C130 plane had taken off from the city of Timika before crashing near its destination of Wamena.
Indonesia's Search and Rescue Agency says the crash site on Lisuwa mountain was been found and the bodies of the victims were being brought back to Wamena.
Indonesia has a patchy air safety record and President Joko Widodo promised a review of the country's ageing air force fleet last year after a military transport plane crashed, killing more than 100 people.
There's been a string of Indonesian air safety mishaps in Papua's mountainous interior in the past sixteen months
Last month, a cargo aircraft crashed in the mountains of Puncak Jaya last month, killing four people
n October, an Air Asia One cessna skidded off a runway in the same area of Puncak Jaya.
The month before that, a Trigana Air plane touching down at Wamena in the Highlands slammed into the runway and lost its landing gear.
In June, a Cessna smashed into several houses near another Highlands airport, at Yahukimo.
In August 2015, a Trigana aircraft crashed in bad weather near Oksibil, killing twelve.