The Victorian doctor who tested positive for the coronavirus has been named as the father of Australian singer-songwriter Missy Higgins.

Dr Chris Higgins, who is aged in his 70s, treated more than 70 patients while ill, prompting concern for his patients at The Toorak Clinic in Melbourne.

Dr Higgins, who is now in isolation, contracted COVID-19 on a recent trip to the US.

He showed symptoms while returning to Melbourne via San Francisco on 29 February.

The doctor's patients, along with staff, have also been asked to self-isolate, while two patients he visited in Malvern's Mecwacare nursing home are also in isolation.

He has also criticised Victoria's health minister for making "unfair" comments about his actions, describing them as a "cheap opportunity for political grandstanding".

Victorian Health Minister Jenny Mikakos said on Saturday: "I'm absolutely flabbergasted that a doctor who has experienced flu-like symptoms has presented to work".

"I understand it was very mild symptoms - perhaps he didn't make the potential link - but we've now got 70 patients that have been contacted. It is incredibly important that all healthcare workers take this matter very seriously."

Replying to a post on the Minister's Facebook page, Dr Higgins wrote: "As the doctor concerned, I have been upset about the inaccuracies and unfairness of your comments."

"This is not the story that I told the DHSS whose job it is to relay information to you," he wrote.

"I had a mild cold when I returned from the USA last Saturday morning which had almost resolved itself by Monday morning, hence my decision to return to work.

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"I hesitated to do a swab because I did not fulfil your criteria for testing but did one anyway on Thursday evening for sake of completeness, not imagining for one moment it would turn out to be positive.

"I believe you have taken a cheap opportunity for political grandstanding and would appreciate an apology."

Doctors rally behind Dr Higgins

Doctors around Australia have been signing an online petition demanding Ms Mikakos apologise for her comments.

A letter from GPs has also reportedly been sent to Ms Mikakos and federal Health Minister Greg Hunt in the wake of the comments.

Australian Medical Association president Tony Bartone said Ms Mikakos' comments were “very unfortunate and disappointing".

“They are a concern to the frontline medical profession who have nothing but the wellbeing of the community and, indeed, their patients (in mind),” he said on Sunday.

Mr Hunt sat on the fence about the need for an apology.

"I'm not criticising anybody. At this point in time we will all be connected to people in shape or form in the coming months, this is a time to come together," he told reporters at Frankston Hospital on Sunday.

"Today is not a day for criticism but for unity."

He also stated the letter was directed to concerns about Victoria, not a call for an apology.

Australia now has 74 confirmed cases of COVID-19, with three deaths.

With additional reporting from AAP.