Thirteen other people were reported wounded. The gunfire broke out at Timika airport when a plane carrying the bodies of two soldiers, believed to have been hacked to death by tribesmen, made a fuel stop.
The soldier, understood to be a friend of one of the two dead men on the plane, was wounded in the leg by other soldiers who returned his fire near an army-run aircraft hangar.
Details of the shooting remained sketchy but the soldier had apparently been assigned to escort the bodies of the two soldiers killed at the weekend in the remote village of Mapunduma.
Jakarta-based diplomats said there was no apparent link between Monday's shootings and the rioting by local tribespeople last month in the mining town of Timika; activists said the rioting underlined resentment towards settlers from other parts of Indonesia who, attracted by the mine, came to live in the town.
Timika and the surrounding area, overlooked by jagged peaks and surrounded by jungle, was tense but calm after the attack which took place ataround dawn.
One Timika resident said: "A soldier at the airport got mad after learning that one of the two dead soldiers had been his friend. He then fired his gun into the people standing there."
Mapunduma, where villagers live in primitive conditions 100 miles from Timika, was the scene of the kidnapping on 8 January of 26 Indonesians and Europeans by separatist rebels .
Eleven of the captives, including four Britons and two Dutch nationals, are still being held in the dense jungle.