Miles said the male had been experiencing abdominal pain, which is not known to be a common symptom of Covid-19.
The second case is an 18-year-old male student at Staines Memorial College, which had been closed over the weekend after another student tested positive for the virus.
All 600 students and staff were sent into isolation last week.
Palaszczuk once again remained firm on the state's border closures, saying there would not be any change in September.
In terms of easing restrictions on gatherings which were imposed last month, Miles has said they would not be eased "for some time".
"That's the kind of the thing we would normally review after one to two incubation periods (of two weeks) of no known infectious person in the community so that's still a number of weeks away," he said.
The tough stance came after Palaszczuk acknowledged there had been some problems with the granting of medical exemptions to people from northern NSW to come to Brisbane for urgent care.
She announced a new unit to help doctors and patients transfer across state lines, which will be running by the end of this week.
It comes as a south Brisbane school remained open on Tuesday despite a positive Covid-19 case having visited the school's after hours care service.
Edens Landing State School opened to students on Tuesday after parents were told an infected person visited the YMCA Outside School Hours Care service operating at the school on August 27.
Queensland Health has deemed the risk to the school as low, according to principal Clint Curren, who issued a letter to parents and the wider school community.
"The Metro South Public Health Unit has assessed the risks to the school community and advised the Department of Education there is negligible risk to members of the school community and it is safe for students and staff to attend the school," the letter read.
One new case was confirmed in Queensland on Monday, bringing the total number of cases related to the Brisbane Corrective Services Academy cluster to 24.