Residents of Fung Hing House in Hing Wah (II) Estate have been ordered to undergo mandatory testing.
The government said it hopes to complete its operation by around 7am on Friday morning.
Earlier on Thursday, health officials said anyone who visited the Deep Water Bay Beach on April 25 and May 1 must also take a Covid test before Saturday.
They said relatives of a woman infected with a Covid-19 variant had held gatherings on the beach on those days.
The city reported two new imported coronavirus cases on Thursday, involving people flying in from the Philippines and Indonesia.