A group of soldiers had been watching over the construction of a bridge in the remote Nduga district, where troops were also attacked last year.
"It happened very quickly, a series of shots were fired from behind the bush. It was a hit-and-run style," Papua military spokesperson Muhammad Aidi said in a statement on Saturday.
A soldier, Usman Hambelo, was hit by a bullet in his waist and died a few hours later, with a helicopter unable to evacuate him due to poor weather, Aidi added.
16 bodies found after attack in Indonesia's Papua
The soldiers called off their hunt for the attackers due to dangerous ravines and dense jungle surrounding the area.
The military believes the attack was orchestrated by the National Liberation Army of West Papua (TPNPB), which claimed responsibility for killing at least 19 construction workers at a remote jungle camp last year, Aidi said.
The employees of state-owned contractor Istaka Karya had been building bridges and roads as part of efforts to boost infrastructure in the impoverished region.
The rebel group was also suspected of being behind an attack in March where three soldiers were shot dead.
Indonesia routinely blames separatists for violence in Papua and conflicting accounts are common.
Jakarta keeps a tight grip on the resource-rich region, which experienced several spasms of violence this summer including the killing of three local people, allegedly by rebels.
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