Two elderly Australians received four times the recommended dosage of the COVID-19 vaccine, but are showing "no signs of an adverse reaction".

The two patients are an 88-year-old man and a 94-year-old woman from the Holy Spirit Nursing Home in Brisbane.

Both residents were given four times the recommended dosage by a doctor working at the facility, who has temporarily been stood down from giving any more vaccines.

Lincoln Hopper, CEO of the nursing home's operator St Vincent's Care Services said that the incident was "extremely concerning" and was reporting the GP to the Australian Health Practioner Regulation Agency.

Hopper also blamed Healthcare Australia, which is contracted by the Australian government to administer the vaccines.

"Yesterday was very distressing to us, to our residents and to their families," Mr Hopper said in a statement.

"This incident is extremely concerning. It's caused us to question whether some of the clinicians given the job of administering the vaccine have received the appropriate training."

"Before vaccinations are allowed to continue at any of our sites, Healthcare Australia – or any other provider – will need to confirm the training and expertise of the clinicians they've engaged so an incident like this doesn't happen again."

Queensland Premier Annastacia Palaszczuk was furious as she told parliament she'd only found out about the overdoses yesterday evening despite the incident occurring in the morning.

"Discovering these details now is simply not good enough. None of this is good enough and the Federal Government must explain itself," she said.

"I want to know what training is being provided to the people the Federal Government is employing to administer the vaccines in our aged care facilities to give additional confidence," she said to 7News.

"People need and must have full confidence in this vaccine."

Federal Health Minister Greg Hunt said that so far, the elderly patients had not had an adverse reaction to the overdose.

"The Chief Medical Officer, who has been involved in that, is in the fortunate position of being able to indicate that all are well and there have been no adverse outcomes," he said.

Hunt also said there were a number of safeguards that were immediately put into place to deal with the incident.

"I think it's very important that we're up front," Mr Hunt said.

"The safeguards that were put in place immediately kicked into action and a nurse on the scene identified the fact that a higher than prescribed amount of the dose was given to two patients.

"I want to thank her for her strength of character and her professionalism."

Queensland began rolling out the vaccine on Monday, with 1,000 people expected to receive the dose by the end of the week.