Premier Annastacia Palaszczuk says the three new cases emerged after 5098 tests in the 24 hours to 6.30am on Thursday.
She says one is a known household contact of a case, another has been infectious in the community for five days, and the third is a woman who has had one dose of a vaccine but has been infectious for four days.
The three new cases are all women aged from their teens to their 30s, and two are unvaccinated, Ms Palaszczuk said.
Two have recently visited Moree in northern NSW, with the third case linked to one of them.
"My message is very clear ... if you are unvaccinated and the virus comes into your community, the virus will hunt you out," she told reporters.
"Now it's really important in Goondiwindi if anyone has any symptoms to please get tested."
Deputy Chief Health Officer Peter Aitken said all three cases are in hospital and will be transferred to a COVID-19 facility, most likely on the Gold Coast.
He said there were a number of household and other close contacts who were in isolation or being tracked down on Thursday.
Dr Aitken said a NSW woman and a Victorian truck driver have also tested positive interstate after being infectious in Goondiwindi.
Deputy Police Commissioner Steve Gollschewski said he was confident restrictions would not need to change because vaccination rates were so high in the town.
Commonwealth figures show that as of Monday, 90.9 per cent of eligible Goondiwindi residents have had one dose of a COVID-19 vaccine and 81.5 per cent are fully vaccinated.
But the high rates are not replicated across the state, and there is concern about some of Queensland's regional communities and vulnerable populations, with more cases expected when borders open.
"Time's running out, we've got to get them vaccinated," Ms Palaszczuk said.
It is understood borders could open sooner than the December 17 deadline if the statewide vaccination rate increases faster than expected.
For Queensland's Indigenous communities, Ms Palaszczuk said part of the problem was the distribution of "misinformation".
"It is wrong, and it is going to have a big impact on communities," she said.
"I'm urging all of our Indigenous Australians to disregard the false information that has been circulated on Facebook and get vaccinated."
AAP with The Project.