The Altona woman worked at Arcare Maidstone on Wednesday and Thursday and may have been infectious at the time.
She sought testing as soon as she fell ill on Friday and was among five new locally-acquired cases reported in Victoria on Sunday.
The facility has been placed into lockdown and residents are self-isolating, with authorities unsure how she picked up the virus.
The woman, a healthcare provider in contact with aged care residents, was vaccinated on May 12.
Unlike the state's hotel quarantine employees, there is no requirement for Victorian aged care workers to get vaccinated.
Some 110 staff work at Arcare Maidstone.
Victoria's Covid-19 Commander Jeroen Weimar said health officials would work with residents' families as they attempt to prevent the virus spreading.
"I'm concerned at this point we don't have an original acquisition source," he told reporters.
"My understanding is at this particular site half the residents were vaccinated and around a third of the staff were vaccinated."
Federal Health Minister Greg Hunt confirmed 53 of the 76 residents had consented to the jab and scheduled vaccinations at the facility were being brought forward from next week to Monday.
"We are encouraging all the residents and families of those who have not provided consent to reconsider and bring themselves forward," Mr Hunt told reporters.
"Around the country, we have seen 85 per cent of residents in residential aged care facilities and 100 per cent of Victorian residential facilities, vaccinated so far."
In a letter to families on Sunday, Arcare said the Maidstone facility had enough protective equipment to maintain patient support. The providers said they were "well prepared" for the lockdown.
Of the other Covid-19 cases diagnosed on Saturday from 45,301 tests, two are linked to Stratton Finance in Port Melbourne and one was a customer at a South Melbourne Telstra store listed as an exposure site.
The fourth case was identified late Saturday night and contact tracers are still interviewing.
There are 49 active cases in Victoria, with authorities uncovering 4000 primary close contacts to date. About 70 per cent of those people have tested negative so far.
Most infections are currently linked to Melbourne's City of Whittlesea cluster, with cases testing positive for the B1617 strain first identified in India.
Acting Premier James Merlino again declined to comment on the status of the lockdown ending on Thursday night as planned, saying no decision has been made and no threshold exists to trigger such an extension.
"We are still in early days," he said.
"This is something that is evaluated every hour of every day."
Masks are mandatory and residents can only leave home to shop for essentials, provide or receive care, exercise, work or study or to get vaccinated.
Wait times at state-run vaccination centres eased on Sunday after the technical issues crippled booking systems.
Despite some waiting up to six hours, 17,702 vaccinations were dolled out on Saturday.
Meanwhile, Victorian Treasurer Tim Pallas announced a $250 million support package to help impacted businesses through the lockdown, which Treasury estimates will cost $700 million.
Mr Pallas lashed the federal government for declining to contribute.
"This idea that we are working hand in glove, when they have never put their hand in their pocket, is nothing short of a disgrace," he said.
