Earlier, Deputy Premier Steven Miles said anyone partaking in panic buying could be further exacerbating the situation.
"We have been in contact with the supermarkets, they are all well supplied," he said on Saturday morning.
"So, anyone rushing stockpiling, it just makes the jobs of our supermarkets and our essential workers in those supermarkets even harder and more risky."
Shoppers have taken to social media to report lines "out the door", with some people reporting waits of up to 30 minutes for a register.
Saturday's new cases are the four family members of a girl whose positive test was announced on Friday, a medical student who tutors the girl, and a staff member from Ironside State School where one of the siblings attends.
They are all confirmed to have the Delta strain.
The source of the latest outbreak remains unclear, however chief health officer Jeannette Young said one of two recently returned travellers had likely given it to an unidentified mystery link who had then passed it on into the community, and to the medical student.
"I think that one of those two cases has led to transmission to someone – who I don't know – which has then led to further transmission and eventually I think the most likely scenario is this medical student has acquired it," she said. "I don't know how."
Brisbane residents have been urged to monitor the Queensland Health website, with exposure sites expected to be added over the weekend.
