But it says that those in "vulnerable areas" close to the coast and on hill tops should move to a safer place.
Emergency accommodation for people already made homeless has been set up at the national football stadium.
The government has warned that heavy rains are forecast for the next six days.
An unknown number of people have been injured and the authorities say they are deploying extra health staff.
As the Ebola virus remains a threat in the country, the clustering of flood victims inside a stadium could pose a new challenge, reports the BBC's Umaru Fofana from Freetown.
The only people exempt from the stay-at-home order, apart from those working in essential services, are school children who are currently sitting their public exams, and a bus service has been set up to take them to school.
But people do not appear to be heeding the order as many are out on the streets, our correspondent says.
The security services have rescued people in some coastal areas where informal settlements have been hardest hit.
The country's main referral hospital, the Connaught Hospital, has also been affected as operations have been cancelled because the theatre has been flooded.
