One healthcare worker was originally identified as having the virus, and contact tracing identified another three who had fallen ill.
Ms Mikakos stressed that contact tracing was a "very, very thorough process" of identifying colleagues and patients who may have been put at risk of infection and that the workers' space has been cleaned.
"There's very strict protocols that apply around cleaning and infection control, so that whole work area where they were, of course, has been thoroughly scrubbed clean," she told reporters on Wednesday.
Stage two of national shutdowns was declared on Tuesday night by Prime Minister Scott Morrison in an effort to curb the spread of the disease.
Weddings will be restricted to the couple, celebrant and two witnesses only, while funerals can only have a maximum of 10 mourners.
Open house inspections and auctions are banned as are personal services such as beauty therapy, waxing, tattoo parlours and massage, to go with the closure of pubs, clubs, cafes and restaurants announced on Sunday.
Premier Daniel Andrews has backed the further closures and crackdown on social functions, telling people "if you can stay home, you must stay home".
'We can't have queues for beds'
Mr Andrews said it was heartbreaking to see people lining up outside Centrelink offices to seek support after losing their jobs.
But the situation could be worse if people don't follow the restrictions aimed at slowing the spread of the virus, so the health system can cope.
"What we don't want is queues for people who need a machine to help them breathe. We cannot have people queuing for intensive care beds. That will mean they will die," he told reporters.
"No dinner party, no shopping trip is worth a life."
The premier has also warned Victorians that restrictions will get more severe and there will be a stage three.
He noted there had been an acknowledgement at the national cabinet on Tuesday that some states would have to ramp up restrictions faster than others.
About 500 police officers will have the daily task of enforcing the closure of non-essential services in Victoria and the mandatory 14-day self-isolation for travellers.
Individuals face fines of up to $25,000 and businesses could be forced to cough up $100,000 for breaching restrictions.
Australians must stay at least 1.5 metres away from other people. Indoors, there must be a density of no more than one person per four square metres of floor space.
If you believe you may have contracted the virus, call your doctor, don’t visit, or contact the national Coronavirus Health Information Hotline on 1800 020 080.
If you are struggling to breathe or experiencing a medical emergency, call 000.