Victoria has gone six days without a local coronavirus transmission, but the Australian Grand Prix has been officially cancelled for a second year.
The health department on Tuesday confirmed there were two new COVID-19 cases in hotel quarantine, bringing the total number of active infections in the state to 25.
But compliance checks on Monday showed three Victorians who returned on travel permits from NSW and Queensland were not isolating as required.
Victorian COVID-19 commander Jeroen Weimar said it was "hugely frustrating" and warned the state might have to stop people on red or orange permits from coming home.
"If you're coming out of a red zone ... we bring you right back into a state that we think has no community transmission at this point," Mr Weimar said.
"We need you to isolate for those 14 days and to work with us to keep the rest of the community safe.
"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."
Acting Chief Health Officer Daniel O'Brien added the health department will investigate the three people and they could be referred to authorities.
It is unclear whether the three people were on red or orange permits.
Victorian health authorities have flagged a possible easing of mask-wearing rules and increasing capacity at stadiums and theatres on Thursday, although plans to return to "COVID-normal" settings could be delayed due to outbreaks in NSW and Queensland.
Victorian Sports Minister Martin Pakula has confirmed 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 COVID-19 restrictions would have eased by then.
But Australia's decision to halve international returned travellers and lagging vaccination rates have forced both events to be cancelled.
"It's very disappointing that these much-loved events can't proceed but this is the reality of the pandemic," Mr Pakula said.
"Until we get much higher vaccination rates we cannot return to more normal settings."
Mr Pakula said discussions were 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.
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.
"We've worked very closely with all of our partners, particularly F1, and indeed the Moto GP as well, but some things are possible in a pandemic and some things are really hard," Mr Andrews said.
Victoria's acting Chief Health Officer Daniel O'Brien said the health department gave no advice about whether the F1 event should go ahead.
"It's a decision between the government and the actual grand prix corporation itself," he said.
He would not detail what input the public health team had into the plans.
The 2020 F1 grand prix at Albert Park was cancelled at the last minute as fans lined up at the gate.
Some 22,149 tests were processed in the 24 hours to Tuesday morning, while 15,451 Victorians received a vaccine dose at one of the state-run hubs.
Just five of the active cases were locally acquired and authorities are confident they have stamped out outbreaks of COVID-19 in the state.
