The woman, from Sydney's southwest, was the only person to test positive over the last 24 hours who wasn't a returning traveller.
Her close contacts have been identified and advised to seek testing and self-isolate.
They include health staff at Liverpool Hospital, Chief Health Officer Kerry Chant said.
"Further investigations are under way to determine the timing of her infection, whether it's a historical infection or a more recent one and there are… her close contacts, including some health staff at Liverpool Hospital, are in isolation pending the outcome of those investigations," she said.
In terms of economic relief, Andrews said there would be further updates "very soon".
"We will have announcements to make very soon," he said. "It's important that we get that package of support right. And we will.
"There's been some discussions – I've had a conversation with the Prime Minister, and had a conversation today with the Federal Treasurer.
"I note he's made a number of comments that I think all Victorians would be very reassured by, that hardship and that real need is going to continue to drive the Federal Government's policy response, just as it always has driven ours and will continue to. We'll make some announcements and we'll do that in good time."
He stressed that "significant economic damage" had been done across the globe.
"This virus is causing enormous damage to jobs, to businesses, to profits, to the state budget and, indeed, household budgets. There's no question about that," he said.
"That's why JobKeeper, JobSeeker, the payroll tax refunds that we provided, the business grants we've provided, and the next package of support that we will very soon announce, are so, so important.
"But it's also, can I say, an important reminder for all of us, that we have to get past this public health bushfire, and get back into a position where we can start to open up again, and start to repair the very significant economic damage that has been done.
"That won't be a quick process in any part of the country. It certainly won't be a quick process here."