Lee Shing House on Lee On Estate has been sealed off since Sunday evening after authorities found the virus in sewage samples there.
A government spokesman said the discovery of the positive cases was worrying.
Five cases were described as “indeterminate”.
The spokesman said the infection risk at the building was very high and the lockdown had to be extended until noon on Tuesday to prevent the virus from spreading.
Residents will be tested again for Covid-19.
The government said anyone who was in the building for more than two hours in the past two weeks must also get tested.
People who do not comply with the testing order risk a fine of HK$10,000, it added.