Residents of Centre Point on Staunton Street are required to undergo compulsory testing.
Health authorities said a man, 27, who arrived here from the United States on Sunday, tested preliminary positive for the L452R mutation.
Prior to leaving for the US from Hong Kong on July 4, he had stayed at Centre Point for about a week and gone to work at Pacific Plaza in Western District.
It was classified as an imported case because authorities said he might have been infected in the US.
The man did not show any symptoms.
Authorities said he had taken both doses of the BioNTech vaccine earlier.
Officials said they hope to complete their operation at Centre Point by 7am on Tuesday.