Three close contacts of the Warrnambool resident, confirmed to be COVID positive on Saturday, have also tested positive to coronavirus.
A man in his 50s is in intensive care at Warrnambool Base Hospital in a satisfactory condition.
The other three people are isolating at home.
South West Healthcare chief executive Craig Fraser said the COVID-19 tracing team detected the new cases are from the same cluster, and other people might ultimately be deemed to be close contacts.
Mr Fraser said he expected to see further cases emerge from the cluster as people's test results become known.
"Warrnambool has done a fantastic job at keeping COVID-19 at bay and we need to continue to do the things that help keep transmissions from occurring," Mr Fraser said.
"That is, adhere to stage three restrictions including wearing a mask, physical distancing, hand hygiene and minimising your movements wherever possible.
"We've seen significant cluster events occur in Melbourne, Geelong and Colac in recent weeks and we must do everything we can to stop a similar large transmission spreading in and around Warrnambool.
"If you feel unwell please stay at home and if your symptoms are consistent with coronavirus get tested.
"We're still in a really strong position in our part of the south west region, we're committed to keeping our communities safe and we appreciate every single person's assistance to help do this."
Warrnambool recorded a new active case of coronavirus on Saturday with the number of overall cases recorded in the city since the start of the pandemic increasing to seven.
Victoria recorded 279 coronavirus cases and 16 deaths in the 24 hours to Sunday morning.
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