The Bell 412 helicopter went down in Kasiguncu village in Poso district, on Sulawesi island, where a radical Islamic group is waging a guerrilla war against the government.
"Twelve (bodies) have been found and identified," said military spokesperson Tatang Sulaiman, adding that rescuers were still searching for one crew member.
The aircraft, carrying seven passengers and six crew, crashed 35 minutes after take-off and just 10 minutes before it was supposed to land, the military said.
Military helicopter crash kills officer, injures two others in Tarbela
There was heavy rain at the time of the accident, and Sulaiman said the bad weather was seen as the most likely cause of the accident.
The military has launched an investigation, he added.
The twin-engine helicopter was purchased in 2012.
The Indonesian military has been hit with repeated aircraft accidents in recent years.
Helicopter crash kills three Afghan air crew
Last month, a small Super Tucano turboprop plane crashed into a densely populated area during a test flight, killing three people.
In December last year two pilots were killed when a military plane crashed in central Java while performing manoeuvres.
And last June, a Hercules C-130 crashed into a residential neighbourhood in Medan, the largest city on Sumatra island, killing 142 people and causing widespread destruction.
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