Two residents - a woman and a man - tested positive at Tafta's Langeler Towers complex on the beachfront, while an elderly woman tested positive at the organisation's Park Care Cottage in Bellair, south of the city.
Shamam said the NICD had been informed.
Last week Tafta took the decision to lock down Langeler Towers and the neighbouring John Conradie House complex - which house about 600 residents.
Some residents, who wanted to continue to run errands like buying groceries and collecting their pensions, objected.
But Shamam said the lockdown was meant to contain the spread of the virus and protect vulnerable residents.
“Everyone is aware that this is the age group most at risk from the disease. We have to act quickly to ensure it doesn't spread,” said Shamam.