The new cases, confirmed by the health department on Monday - the fourth day of the state's seven-day lockdown - brings the total number of locally acquired cases to 45.
Some 43,874 Victorians were tested in the 24 hours to Monday morning, while 16,752 COVID-19 vaccine doses were administered by the state government during the same period.
It comes as two aged care workers and a resident have tested positive for COVID-19, after a worker at an Arcare aged care home in Maidstone returned a positive result on Sunday.
"Arcare can confirm that unfortunately a second team member and one resident at its Maidstone residence have tested positive to COVID-19," Arcare chief executive Colin Singh said in a statement on Monday.
"The resident is displaying mild symptoms however we are transferring them to hospital where their condition can be closely monitored. The team members also have mild symptoms and are recovering at home."
Mr Singh said the resident received one dose of the Pfizer vaccine and was awaiting a second dose.
Arcare Maidstone was locked down and residents were placed into self-isolation on Sunday after a staff member at the facility, a woman in her 50s, tested positive for the virus.
The Altona woman had received her first dose of the coronavirus vaccine on May 12. It is possible she was infectious during shifts on Wednesday and Thursday.
The second team member did not get the jab as she was "on personal leave" when vaccinations took place.
Contact tracers are yet to uncover how the first worker caught the virus, making her a "mystery case".
Only a third of Arcare Maidstone's 110 staff and 53 of 76 residents have been vaccinated so far, with the federal government bringing forward scheduled vaccinations to Monday.
Federal MP Bill Shorten, whose electorate of Maribyrnong takes in the facility, said most residents and staff were yet to receive their second dose of the vaccine.
"The people who are sick had actually had a vaccination. You need two. One is not enough," he told ABC News Breakfast on Monday.
Health Minister Greg Hunt said 85 per cent of residents in private aged care facilities and 100 per cent in Victorian residential facilities have been vaccinated.
Australian Nursing and Midwifery Federation Victorian branch secretary Lisa Fitzpatrick said vaccination rates at the Maidstone facility demonstrated Canberra's "go-slow culture" on aged care.
"The hindsight of almost 2000 Victorian aged care residents contracting COVID-19, 655 resident deaths and more than 1600 aged care workers infected was not enough to motivate the Morrison government into urgent action," she told ABC Radio.
It is also being reported a female worker at BlueCross Western Gardens in Sunshine, in Melbourne's western suburbs, has tested positive for COVID-19.
The staff member was a close contact of one of the Arcare Maidstone workers.
Meanwhile, Royal Freemasons has locked down its Coppin centre and Footscray facilities after it was notified a staff member had worked at Arcare Maidstone.
More than 600 people living in aged care homes died last year as a result of Victoria's second wave of COVID-19. The majority contracted the virus from staff, many of whom were working across multiple facilities.
There are now 290 locations on the state's list of exposure sites, including a soft drink factory in Thomastown, a number of bus routes in Melbourne's north and various stores at Chadstone shopping centre, as well as Arcare Maidstone.
Craigieburn's Willmott Park Primary School was closed on Monday with nearby Mount Ridley College listed as an exposure site after a pupil tested positive for COVID-19 on Saturday.