Prime Minister Manasseh Sogavare called for the lockdown in an address that was broadcast late on Wednesday, after police had earlier deployed tear gas to break up protests.
People from the country's most populous island, Malaita, had travelled to the capital in a spillover of anger about a host of domestic issues including unrealised infrastructure promises, media reported.
As well as anger about a lack of development, the Solomons government has faced pressure over a 2019 decision to cut ties with Taiwan and establish a formal relationship with China.
"Our nation witnessed another sad and unfortunate event aimed at bringing a democratically elected government down," said Sogavare.
"I had honestly thought that we had gone past the darkest days in the history of our country, however today's events are a painful reminder that we have a long way to go."
A lockdown in Honiara, which would run until 7am on Friday, local time, "will allow our law enforcement agencies to fully investigate the perpetrators of today's events and to prevent further lawless destruction," he said.
As well as looting stores, demonstrators set fire to a thatched roof building on the grounds of the parliament - as it was sitting - and a police station, said the prime minister.
The Royal Solomon Islands Police Force (RSIPF) urged people attending schools and businesses around Honiara to stay home to avoid being affected by unrest.
"We want to make sure that our streets, schools and businesses will reopen soon after the lockdown," said RSIPF deputy commissioner Juanita Matanga in a statement.
"I am asking for your cooperation until the situation turns normal."
