The clashes, which began Feb 29 near the Grasberg copper and gold mine in Papua province, had previously killed a police officer and injured three others. Police said the attackers are believed to be members of the West Papua Liberation Army, the military wing of the Free Papua Organization.
Rebels in Papua have been fighting a low-level insurgency since the early 1960s, when Indonesia annexed the region, which was a former Dutch colony. Papua was formally incorporated into Indonesia in 1969 after a U.N.-sponsored ballot that was seen as a sham by many.
Mimika district military chief Lt. Col. Pio Nainggolan said the soldier was hit by a bullet when he was preparing for dawn prayers and died at a hospital hours later.
He said a joint military and police force was hunting "an armed separatist criminal group."
"We are on the highest alert as instructed to all troops on the ground," Nainggolan said in a video obtained by The Associated Press.
The mine, which is nearly half owned by US-based Freeport-McMoRan and is run by PT Freeport Indonesia, is seen by separatists as a symbol of Indonesian rule and has been a frequent target for rebels.
The current shootout in the mining town of Tembagapura has caused about 2,000 villagers to flee for safety to neighbouring Timika city.
Attacks by rebels near the Grasberg mine have spiked in the past year.
The Grasberg mine's vast gold and copper reserves have been exploited for decades by Freeport-McMoRan, damaging the surrounding environment while providing significant tax income for the Indonesian government.
But indigenous Papuans have benefited little and are poorer, sicker and more likely to die young than people elsewhere in Indonesia.