It takes the state's current outbreak to about 80.
The results were detected among 24,265 tests received on Sunday, and there were 17,719 vaccine doses administered at state-run sites.
Victoria's Deputy Chief Health Officer Allen Cheng yesterday said the state was running "neck and neck" with the outbreak when it came to managing the "downstream" risks of positive cases emerging from already identified exposure sites and chains of transmission.
He said health authorities were more concerned about the "upstream" risk posed by the Delta strain West Melbourne outbreak, given the source of infection for the earliest recorded cases remained unknown.
Two of the cases in today's update from the health department were revealed yesterday, and emerged at the Arcare Maidstone aged care facility.
Arcare said the cases involved a 79-year-old resident and an agency registered nurse who last worked a shift on Saturday.
Arcare's chief executive said all team members who worked at Arcare on Saturday were required to get tested immediately and quarantine for 14 days.
More than 200 primary close contacts linked to a construction site in Melbourne's CBD were being tested yesterday as a priority.
The site, in Queen Street, is listed as a Tier 1 exposure site.