Videos on social media show police firing tear gas to disperse looters, and buildings on fire.
RNZ Pacific's correspondent in the capital Honiara, Georgina Kekea, was in the Kukum area where the police station and shops were set alight, and said at least one building had been burned down.
Police she spoke to said the large crowds had been at the other end of town, and officers had not expected the crowd to attack their police station.
"So when they came out and they just saw all the protestors there and they had to run into a room and hide. There were about 10 of them. They were in the rooms when they started breathing in smoke and they realised that the building was being burnt, so they came out and the building has [now] burnt down," she said.
Earlier in the day a plume of black smoke was seen rising from parliament's grounds, where Kekea said a leaf hut used for coffee breaks was on fire, before firefighters from the fire station next to parliament put the blaze out.
Kekea said local police are calling for calm as they tried to restore order.
They said much of the looting was being carried out by criminal opportunists, most of them young men.
The original protest at parliament was led by citizens from Malaita Province, who were voicing their frustrations in the national government and calling for the prime minister Manasseh Sogavare to step down.