Official advice from the World Health Organisation remains that personal protective gear such as such as gloves, P2 or N95 masks, goggles, face shields and gowns must be prioritised for clinicians treating COVID-19 patients, due to global shortages.
With data from China suggesting as many as four out of five people carrying the virus had no symptoms, Dr Hackett said, hospitals should begin testing all healthcare workers and removing anyone who tests positive.
"There will be a lot of asymptomatic staff just transmitting the disease," Dr Hackett said, urging hospitals to operate "as if at least 20 per cent of people in there have got coronavirus".
"You need to treat this virus with the respect it deserves," he said. "Everyone's a COVID patient until proven otherwise."
He said hospital workers "shouldn't be going home right now" and that Australia should follow China's lead in housing them in hotels.
On Friday, Victorian health authorities revealed the rate of infection among the state's healthcare workers had almost doubled in a week.
Authorities have offered doctors and nurses who do not want to put loved ones at risk the option of staying in a hotel, but at this stage only those who either test positive or have been exposed to a patient with COVID-19 without the right protective equipment are being given access.
Undetected coronavirus cases have infiltrated hospitals in NSW, Victoria and Tasmania, from the oncology ward at Melbourne's Alfred hospital - where three cancer patients died of COVID-19 - to the radiation ward at Sydney's Westmead hospital.
Federal Health Minister Greg Hunt said this week Australia was succeeding at "flattening the curve" of the pandemic in the wake of heightened social distancing rules.
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But Dr Hackett argued the government would not know how many people were spreading the virus in the community - including those without symptoms - until it had collected data from a sufficiently broadened testing regime.
Mr Hunt also announced the arrival in Australia of 11 million protective masks for healthcare workers, including seven million for the nation's hospitals.
Australian Healthcare and Hospitals Association chief executive Alison Verhoeven said hospitals were "working very hard at infection control" to prevent the coronavirus from spreading through wards, giving staff extra training and implementing strict cleaning strategies.
"In an ideal world we wouldn't have to be rationing supplies, but the reality is that that has had to happen," Ms Verhoeven said.
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Hospitals have introduced temperature checking and restricted visiting hours, with many banning visitors altogether in high-risk wards such as intensive care units.
Australian Medical Association Victorian president Julian Tait said adequate personal protective equipment and proper training in its use was essential.
While "many hospitals have this covered", Dr Tait said, "some don't - and they have to lift their game."
The AMA's NSW president Kean-Seng Lim said authorities should be aiming for "zero healthcare worker deaths" and that protecting staff was not just about PPE, calling for improved access to telehealth for hospital clinicians who wanted to treat patients remotely.
"Whatever can safely and appropriately be done by telehealth or virtual consultation should be," Dr Lim said.
"Our members tell us that this is not always happening."
Dana is health and industrial relations reporter for The Sydney Morning Herald and The Age.