Many businesses remained closed in Honiara ahead of the vote over concerns that violence could erupt again, leading to an eerie calm.
Troops and police from Australia, Papua New Guinea, Fiji and New Zealand are helping keep the peace at the request of the Solomon Islands government.
The riots grew from a peaceful protest that highlighted long-simmering regional rivalries, economic problems and concerns about the country's increasing links with China.
Opposition leader Matthew Wale told Parliament he brought the motion of no-confidence against Prime Minister Manasseh Sogavare because a political solution was needed to the nation's problems. He said he had some misgivings.
“I am conscious that what we say in ventilating this motion may further add to what are already high levels of anger in certain quarters of our society,” he said.
Wale and other lawmakers spoke at length, using a mixture of English, the official language, and the commonly spoken Melanesian pidgin.
Lawmaker Rick Hounipwela also argued that Sogavare needed to go, saying there had been an increase in corruption and that the prime minister was blinded by “anything that glitters”.
“Given this track record, who knows? If someone else maybe come and give him a better offer,'' Hounipwela said, “I'm sure he's very capable of throwing out even China.” Other lawmakers expressed support for Sogavare.
Health Minister Culwick Togamana said the government had been democratically elected and changing it now would vindicate the rioters, proving that the ends justify the means.
Togamana said evidence of the government's effectiveness could be seen by the fact there was no community spread of the coronavirus.
The Solomon Islands has reported just 20 cases of the virus and no deaths.
The riots and looting targeting Honiara's Chinatown and downtown precincts erupted Nov 24 following a peaceful protest in the capital by people from the province of Malaita. Police fired tear gas and rubber bullets at the demonstrators, who set fire to a police station and many other buildings.
Critics also blamed the unrest on complaints of a lack of government services and accountability, corruption and Chinese businesses giving jobs to foreigners instead of locals.
Sogavare angered many in 2019, particularly leaders of Malaita, when he cut the country's diplomatic ties with Taiwan to recognise China instead.
Daniel Suidani, the premier of Malaita, said Friday he thinks the Solomon Islands should partner with Taiwan because they share democratic values.
The Solomon Islands has a population of about 700,000 and is located northeast of Australia.