Health Minister Yvette D'Ath said the woman entered Queensland on June 5, passing through Goondiwindi and Toowoomba.
She is staying with family at Caloundra, including her husband, who has so far tested negative.
"The woman was tested yesterday and, it was confirmed today, that it was a positive case," D'Ath said.
Queensland's chief health officer Dr Jeanette Young remained calm and did not lambaste the couple for leaving Victoria during lockdown.
She said there were more than half a dozen exposure sites, including a McDonald's in Goondiwindi, a service station in Toowoomba and the women's section at Kmart in Caloundra, over three days.
"I don't know the details of why they left or what the reason was," Dr Young said.
"Of course we will be looking into how all this happened."
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She said contact tracers had so far identified six close contacts and while her husband has not tested positive, he is being monitored in Sunshine Coast University Hospital.
Dr Young said the woman developed symptoms on June 3 and empathised with Queenslanders about the positive case.
"She has been out and about since she arrived – since June 5," she said.
"Any case of Covid is frustrating.
"The community has had to put up with so much now for 18 months and to do this again, it doesn't matter the cause, any community case of Covid is going to be frustrating for a lot of people."
Queensland Police Deputy Commissioner Steve Gollschewski said the couple's movements would be examined and they would be questioned on their reasons for travelling into Queensland while Victoria was declared a hotspot.
In the meantime, their prime concern was contract tracing and to determine who has been exposed to the virus, he said.
"Of course we are going to investigate the circumstances of what's happened here," Commissioner Gollschewski said.
"We've got a couple that have come from Victoria when Victoria is in a lockdown.
"All the aspects of how that's occurred, including what's happened in the other states, we will do in a cooperative manner with our colleagues in Victoria in New South Wales.
"We'll examine all those issues around passes, whether they are appropriate and what has happened – it is too early to say.
"The whole purpose of our investigation will be to establish the facts."
