The Department of Health and Human Services has confirmed the six cases, two of which were tested at GV Health, and two at Yarrawonga Health.
GV Health chief executive Matt Sharp said both people who tested at the hospital recently returned from overseas and were assessed after developing flu-like symptoms.
"One person was subsequently assessed in GV Health’s Acute Respiratory Clinic and the other person was assessed by their GP with the testing swabs subsequently sent to GV Health’s Pathology service," he said.
"Follow-up care and contact tracing is being undertaken by the treating doctors and the Department of Health and Human Services. It is understood these people have been self-isolating and will now be in quarantine.
"I cannot stress how important it is for people to follow the directions from the Victorian Government and health care clinicians regarding what is required when people are self-isolating, in quarantine and the importance of social distancing.
"Everyone is responsible for limiting the spread of COVID-19 and particularly people who have a higher risk of passing on COVID-19."
At this time, there are no inpatients at GV Health who have tested positive for COVID-19.
No details have been provided regarding prior movements and where the person is from within Moira Shire.
On Friday, Yarrawonga Health confirmed a second positive case of COVID-19, after a person presented to the hospital earlier in the week.
Yarrawonga Health confirmed their first case on Tuesday.
The two individuals who were tested had returned from overseas and were following self-isolation requirements when they developed flu-like symptoms.
They were both well enough to return home after being assessed by the hospital, and have been continuing home quarantine.
NCN Health could not confirm on Saturday whether they had tested a positive case of COVID-19 at one of their hospitals.
The total number of coronavirus (COVID-19) cases in Victoria is 685 – an increase of 111 from Friday.
Victoria has recorded three deaths related to COVID-19. There have been no new deaths recorded overnight.
The total number of cases includes 378 men and 300 women, with people aged from eight to 88.
There are 21 confirmed cases of COVID-19 in Victoria that may have been acquired through community transmission.
More than 30,100 Victorians have been tested to date.
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