The shooting took place at a market in Sinak in Papua's Puncak Jaya regency.
A Highlands-based Defense Region Command of the rebel group, which says it is waging a war for West Papuan independence from Indonesia, made a statement about the attack.
A spokesperson confirmed a team of his men shot the soldier dead.
He said the shooting was a message to the government of Indonesia and the global public that the West Papua National Liberation Army would not cease to oppose the military and the Indonesian police.