Victorian authorities are threatening to shut the border to red zone returnees if they continue to go walkabout, as two international motorsport events were again cancelled.
Of 231 home compliance checks on Monday, three Victorians returning from interstate hotspots were found not isolating as required.
The state's COVID-19 commander Jeroen Weimar said it was "hugely frustrating" and warned the state might have to suspend its red zone permit system.
"We need you to isolate for those 14 days and to work with us to keep the rest of the community safe," he told reporters on Tuesday.
"Because otherwise we won't have any choice but to not allow people to come back home, and that's the last thing we want to do."
A Victoria Police spokeswoman confirmed to AAP it was investigating after reports three people failed to self-isolate in line with red zone permit directions.
It comes as the Victorian government announced the Australian Grand Prix in Melbourne and Australian MotoGP at Phillip Island will not go ahead later this year.
The 2021 Formula One event had already been pushed back from its regular early season timeslot to November in the hope restrictions on international arrivals would ease by then.
But Sports Minister Martin Pakula said last week's national cabinet decision to halve international returned travellers and lagging community vaccination rates made it unfeasible to host the events.
"We're simply not in a position to give F1 management or MotoGP the sorts of guarantees and assurances and comfort that they need this week," he said.
Mr Pakula said discussions were already underway with F1 organisers to host the 2022 grand prix in April.
"It's unlikely to be the first race next year but, frankly, that probably suits us," he said.
Mr Pakula is confident the 2022 Australian Open will be unimpeded as it vies to return to its traditional January timeslot.
Premier Daniel Andrews earlier said once 70 to 80 per cent of Victorians were vaccinated, the state would have the "protection, freedom, choices and options" to run big international events.
"Some things are possible in a pandemic and some things are really hard," he said.
Opposition upper house leader David Davis said the F1 event gave Victoria a "massive economic boost" each year and could have proceeded safely.
"If he (Mr Andrews) had confidence in his hotel quarantine, if he had a proper plan, he would have been able to go ahead," he said.
Acting Chief Health Officer Daniel O'Brien confirmed the public health team gave no advice about whether the F1 event should go ahead, although it did have input in the now-abandoned plans.
The 2020 Australian Grand Prix at Albert Park was sensationally cancelled at the last minute as fans lined up at the gate.
In the 16 months since then, the Victorian events industry has been decimated by four statewide lockdowns that have dented Melbourne's claim as the events capital of Australia.
Save Victorian Events said the answer to their financial woes lies in more modest-sized events, rather than major events which make up just five per cent of the state's $12 billion-plus industry.
"It is about using events to rebuild Victoria from the ground up. This should be the basis of Victoria's event-led recovery," it said.
Victoria racked up its sixth straight day without a local coronavirus case on Tuesday, bringing the total number of active infections in the state to 25.
Two new cases were also detected in hotel quarantine.