Eleven evacuation centres have been set up at schools and at Honiara's international airport, said the World Vision aid agency.
The domestic airport terminal is under water and there are fears about the spread of disease once the water subsides.
It is feared that the floods have caused millions of dollars worth of damage to the islands' infrastructure.
Other parts of Guadalcanal province - where the capital is located - have also been declared disaster zones, officials say.
"Clean water sources have been contaminated, sanitation facilities destroyed and there is a lack of medicines to treat people who get sick," said Lawrence Hillary, World Vision's emergency response manager.
Water levels were reported to be subsiding yesterday, allowing debris to be searched for bodies. The impact of the flood was made worse because it struck so fast, giving people little time to escape from their homes.
"I witnessed a mother and two children swept away in their home," Paul Lega told the Solomon Star. He said the devastation was the worst disaster the nation has seen.
Save the Children said the scale of the damage was still unclear outside Honiara as both bridges out of the city had been cut off. In the city thousands of homes have been washed away.
Damage caused by flooding in Honiara is estimated to run into millions, the Star reported.
New Zealand has given an initial contribution of $300,000 and Australia has pledged at least A$50,000 ($54,000) to support relief efforts.
