"It's important we're upfront."
Hunt said the patients were being monitored and no adverse reactions had been reported so far.
"This is an individual practitioner who has clearly made an error and around the country - and you will remember from multiple press conferences, I've indicated that whether it's the flu, whether it's other things, during the course of any one year, there would be challenges, issues and errors," he said.
"Ordinarily they wouldn't necessarily be focused on. They'd be dealt with through the ordinary measures.
"Because of the national focus on this, it's natural and understandable that those things which would ordinarily occur are given greater prominence.
"I absolutely understand that and, indeed, I've made the decision that I thought we should address this up-front to show that the safety guards that were put in place did actually work."
Hunt said while there was "an initial error", three safeguards were immediately kicked into place.
"Firstly, the nurse on scene responded," he said.
"Secondly, the company responded, and thirdly, the health care agencies, the cooperation between the Commonwealth and Queensland responded."
Chief Health Officer Professor Paul Kelly said while the patients received a "maladministration" of the dose, there were a couple of points to make.
"Firstly in the early clinical trials of the Pfizer and BioNTech vaccine, they did actually experiment with different doses of the product, including one three or four times higher than what have eventually been the prescribed doses," he said.
"During those trials, the side effect data was not a higher problem, so there's that element. "Second of all ... we are aware of several cases like this happening early in the phased rollout through residential aged care facilities in Germany and the UK.
"Again, the side effect profile was minimal, particularly in older people, so that gives us hope."
Professor Kelly said when he was informed of the incident just after midnight, they took immediate action.
"I was assured that everything that had been done on the site was what we would have expected and that a full incident reporting system had been actioned," he said.
