At least four buildings were looted and torched on Friday and there were further disturbances again on Saturday.
Solomon Islands police are holding 15 people in custody. Another 35 have been released on bail but a police spokesman says further arrests are likely.
Riot police are still patrolling the streets after the city returned to calm on Sunday.
According to reports, a crowd of more than 400 people started looting in an area near the King George sixth secondary school in eastern Honiara on Friday night.
Police say most of the rioters were people affected by last month’s flood disaster, who are unhappy with the government’s relief programme.
The rioting occurred on both Friday and Saturday nights and police needed tear gas to subdue the offenders.
The rioters left a shopping centre badly burnt and palm trees along a key street destroyed.
RNZI correspondent Dorothy Wickham says it is clear at least some of the rioters are victims of last month’s floods and had been at an evacuation centre at the National University.
She says several businesses, mostly owned by Chinese, were wrecked but the initial target was the bottle shop in the complex.
“So they raided that first, took out all the alcohol, went off and drank it, got more drunk and then came back and lit the place on fire. That is the sequence of events that I understand.
Early reports said the rioters were reacting to moves by the National Disaster Management Office and international relief agencies to shut down the remaining evacuation centres.
But Barnabas Hanson, the interim chair of the Joint Civil Society Groups and Concerned Citizens, says that’s not true.
“I have spoken to the chairman of the flood victims’ interim taskforce and he’s confirmed to me that the victims are remaining in the camps,” he said.
“They have been advised not to participate or to join any groups that would like to engage in unlawful activity.”
Interim chair of the Flash Flood Victims Coalition Taskforce, which is representing the interests of flood victims in the evacuation centres, says people from the camps were not involved.
Though Jeffrey Leni says people who had already been repatriated may have taken part.
The country manager for World Vision, the largest non government organisation providing flood relief in Solomon Islands, says it is not clear what sparked the rioting and looting. Andrew Catford says they hope it was an isolated incident.
“There were perhaps a few people who came from the evacuation centres who had some complaints but also quite a lot of people from Burns Creek area, which is neighbouring a few of the evacuation centres.
“Quite a lot of unemployed people there, particularly youth, who perhaps saw this as a little bit of an opportunity to create a little bit of trouble.
Matthew Quan, from the Chinese Association of Solomon Islands, says rumours have been circulating that there could be more riots, which prompted him to close his shop in Chinatown for several hours.
He said other businesses have also closed their doors as a precaution against possible rioting.
“What I’ve heard is down in Honiara all the shops are closed, including all the banks and offices as well.
“In Chinatown, we received word and everyone proceeded to close their doors – including ourselves.”
Meanwhile, Australia’s Department of Foreign Affairs has warned Australians in Honiara to exercise a high degree of caution, avoid protests or large gatherings and minimise travel at night.
It says further civil unrest is possible over the next few days.
Six weeks ago, Honiara and the eastern plains of the island of Guadalcanal were devastated by floods that left 23 people dead.
Between 50,000 and 60,000 people – half the island’s population – were left homeless.
More than 4000 people remain in temporary evacuation centres.