Management from Baptcare Westhaven, an aged care facility in Footscray, confirmed there have been 35 cases of COVID-19 in the home since an outbreak began on November 12.
Six residents have since died with the virus.
According to Baptcare, 31 of the cases are residents while four are employees or contractors who work in the home.
There are currently 25 positive residents in the home, and four are receiving care in hospital.
The vaccination rate among residents at Westhaven is 90 per cent, while all employees and contractors are fully vaccinated.
Four of the positive residents were not fully vaccinated.
Visits to the facility have been banned except for under exceptional circumstances.
"The health, safety and wellbeing of our residents, employees and community is our highest priority," Baptcare Westhaven said in a statement.
"We do this by implementing strict infection prevention and control measures and following the guidance and advice from the Department of Health and Western Health Public Health Unit."
Management has said it is being supported by members of the Royal Melbourne Hospital medical and nursing teams who are attending Westhaven daily.
"We understand the impact that this has on our residents and their families and are doing all that we can to limit the spread of the virus," the statement reads.
"We are communicating daily with all families of residents and providing them with information during this challenging time."