Victoria's Chief Health Officer Brett Sutton confirmed on Monday a young woman tested positive to COVID-19 after attending the June 6 rally.

He said it was "very unlikely" she would have contracted the virus at the rally or transmitted it to others as she wore personal protective equipment and had mild symptoms.

"(She) took a great deal of care in terms of having a distance with others and I think is unlikely to have acquired it there given that there are a whole number of other places that this individual has gone to without PPE," Prof Sutton told reporters.

While he was "not convinced" there had been community transmission at the Black Lives Matter protests, Prof Sutton urged anyone who has developed coronavirus symptoms to get tested.

"It's really in that first week that people overwhelmingly develop symptoms, so any cases really should be out there now," he said.

The protester was one of 12 new coronavirus cases recorded in Victoria on Monday.

Seven of the new cases are linked to one extended family and include four schoolchildren, prompting the closure of Pakenham Springs Primary School and St Dominic's Primary School in Broadmeadows for deep cleaning and contract tracing.

A total of 11 family members across different households in Broadmeadows, Coburg and Pakenham have contracted the virus, with the source of the original infection in the cluster still under investigation.

"The extended family is very large," Prof Sutton said.

"They've had gatherings across different households as many of us do now."

He said the family cluster was a lesson to families to restrict their movements if they are feeling unwell.

Two other cases recorded on Monday were linked to a patient of Monash Health, who tested positive on Sunday.

Additional cleaning has been undertaken at the hospital and close contacts of the infected patient are in quarantine, a Monash Health spokeswoman told AAP.

"No services have closed due to this incident," she said.

Despite the double-digit increase in new cases, Prof Sutton remains confident restrictions will be eased on schedule next week.

Cafes, restaurants and pubs will be able to increase their capacity from 20 to 50 patrons from 11:59pm on Sunday, while cinemas, gyms and theatres have been given the green light to reopen.

Children will be able to compete in contact sports, while non-contact sport will also return for all age groups, as will skiing, with the season to start from that date.

VICTORIA'S 12 NEW CORONAVIRUS CASES:

*Young woman who attended Melbourne's Black Lives Matter protest

*Two people linked to a hospital patient, including a healthcare worker

*Seven people linked to a family outbreak, including four students

*One returned traveller in hotel quarantine

*One case under investigation.

Australian Associated Press