Testing commander Jeroen Weimar said the case was “extremely concerning”.
The woman worked at Arcare in Maidstone on Wednesday and Thursday.
The facility is now under an additional lockdown with residents confined to their rooms.
“I can confirm that this facility has been on the Commonwealth program for vaccination, over half the residents have been vaccinated, and we believe about one-third of the staff have been vaccinated,” he said.
“This individual positive case member has had her first vaccination dose.
“Again, we got strong records with this particular facility and my thanks to them, but I would please encourage anybody who has got any connections with ArcCare in Maidstone on Thursday the 26th of May and Friday the 27th of May – to please get in touch immediately, isolate and get tested.
“I want to thank the worker for doing the right thing and getting tested immediately upon getting symptoms, and helping get the facility as safe as possible.”
In total, two of today’s five cases are close contacts in quarantine, one is linked to an exposure site and two are under investigation.
Mr Weimar said it was worrying the aged care worker’s case at this stage did not have a traceable source.
“I am concerned that at this point in time we don’t have an original acquisition source,” he said.
“The Western health public health team are working very hard to identify that acquisition source and we will be doing genomic testing.
“At this point in time this is the biggest priority for us to make sure we fully understand and wrap ourselves around both where the cases come from and where those chains are.”
The testing chief added that it was the first mystery case since the latest cluster.
“I think at this point in time, this is the first mystery case we have seen in this particular outbreak,” Mr Weimar said.
“This one case is currently not linked … but of course is a significant concern for us and we will get everybody focused on trying to identify where it has come from and any exposure she may have had.”
Mr Weimar said authorities would be working throughout the day investigating the aged care infection.
“It is the most important of our cases today – the mystery case in the aged care facility – and it will be a real focus for us in the hours ahead.”