For almost two weeks, the region has been racked by civil unrest over perceived racial and ethnic discrimination, although some protesters are demanding an independence vote.
Protesters torched a building housing the offices of state-controlled telecoms firm Telkomunikasi Indonesia . However, in a statement on Thursday, the company said it could not identify the damage yet.
The PLN utility has turned off power in areas around the torched building, Ahmad Rofik, its regional director for Maluku and Papua, told Reuters.
Police fired tear gas to scatter demonstrators who set fire to cars and threw stones at shops and offices, state news agency Antara said, adding that protesters also set on fire a local parliament office.
"Several public facilities and properties were damaged by rioters," said national police spokesman Dedi Prasetyo. "Authorities are trying to control the situation."
State energy firm Pertamina shut several gas stations in Jayapura over the protest, its spokesman, Fajriyah Usman, said.
Shooting broke out a day earlier between protesters and police in the town of Deiyai, about 500 km from Jayapura. Police said one soldier and two civilians were killed in the incident, while a separatist group said six had been shot dead, a claim the military dismissed as a hoax.
Police have deployed 300 mobile brigade personnel to the towns of Deiyai, Paniai and Jayapura after Wednesday's incident, the news agency quoted police chief Tito Karnavian as saying.
A separatist movement has simmered for decades in Papua, while there have also been frequent complaints of rights abuses by Indonesian security forces.
The spark for the latest unrest was a racist slur against Papuan students, who were hit by tear gas in their dormitory and detained in the city of Surabaya on the main island of Java on Aug. 17 for allegedly desecrating an Indonesian flag.
The government has cut internet access in the region since last week to stop people sharing "provocative" messages that could trigger more violence, a step criticised by rights group and journalists, who said it had made reporting difficult.