Sometimes violent protests convulsed the region for two weeks in late August over racial slurs against Papuan students in Java's city of Surabaya, who were tear-gassed in a dormitory and detained over accusations of desecrating a national flag, Presstv Reported.
The soldier was stabbed to death after escorting student protesters from a demonstration at a local university in Jayapura, the military said in a statement.
The students had been taken away in trucks by security forces after police and the university prevented them from holding a protest at the campus, the statement said.
Kompas TV reported three students were also killed in the clash, citing the head of Papua province health department. A police spokesman did not immediately respond to a request for comment on the report.
Media said the student demonstration was led by returnees from other parts of Indonesia.
Elsewhere in Papua, Indonesian security forces were battling to restore order in Wamena, the biggest town in the highland interior of Papua province, after buildings were set ablaze.
Papua police said the clash started after a fight between students from two different schools in Wamena.
"The fight then escalated to burning of government and public facilities as well as private properties in Jayawijaya regency," they said in a statement.
"Security forces from the military and the police are still trying to calm the masses."
There was "chaos" in Wamena, state news agency Antara quoted district police chief Toni Ananda as saying. The agency cited another official as saying the town's airport had been shut.
One of Indonesia's biggest news portals, Kompas.com, earlier said the violence was triggered by racist slurs directed at students by a teacher in Wamena, but Papua police said this was not true following checks with teachers and the school.
Resource-rich Papua - which is home to the world's biggest gold mine and its second-biggest copper mine Grasberg - was a Dutch colony that was incorporated into Indonesia after a controversial UN backed referendum in 1969.
The region has since endured decades of mostly low-level separatist conflict.
After the August protests began, Indonesia sent about 6,000 additional military and police personnel to the region, and authorities blocked internet access for a time to prevent use of social media.
Police have rounded up dozens of people for damaging public property in the protests, with several named as treason suspects over a demand for an independence referendum that authorities have ruled out.