The worker had also received the first dose of the vaccine, and more than half of the residents at the facility have been vaccinated.
Contact tracing is under way to determine how the worker caught the virus.
"This is the first mystery case we have seen in this particular outbreak," Weimar said.
"We have identified the infectious period as potentially being Wednesday and Thursday of this week, the 26 and 27 of May, and of course we have now put in place our full response.
"We are doing on-site testing, of course."
The aged-care centre has gone into strict lockdown, with residents confined to their rooms.
Five new cases today
Victoria recorded five new local cases of Covid-19 on the third day of the state's lockdown, including the aged-care staffer.
One returned traveller in hotel quarantine also tested positive. There are now a total of 49 active cases in the state.
People continue to turn out for Covid tests in droves, with 45,301 swabs taken in the past 24 hours.
More than 17,700 doses of the Covid-19 vaccine were administered.
Two of the five cases were close contacts of other cases, with links between the other three new cases — including the aged care worker — and previously known cases being investigated.
One was linked to a known exposure site, Merlino said.
Anti-lockdown protest
It comes after police arrested 14 people and pepper spray was used at an anti-lockdown protest in Melbourne on Saturday.
There are only five reasons Victorians are allowed to leave their homes for seven days: shopping for essential goods and services, caregiving, exercise, authorised work and study, and to get a Covid-19 vaccination.
The state government has empowered police to issue on-the-spot fines of A$1652 ($1756) for individuals who don't comply with the emergency restrictions.
People who don't wear masks also risk A$200 fines.
Under current plans the last day of lockdown will be Thursday, with the possibility of some restrictions extending beyond that, or the dates to change depending on the latest numbers.
The state recorded five new local coronavirus cases on Saturday, four on Friday and 12 on Thursday.