Victoria's health department confirmed on Tuesday afternoon it had been notified of a further four cases.

All are family contacts of a man in his 60s, who became the fifth person in Melbourne's northern suburbs to test positive.

Victorian Chief Health Officer Brett Sutton said authorities were working to contain the outbreak, with 84 of 164 primary close contacts testing negative so far.

"We have to chase down every single close contact ... but it's certainly not out of control," he told ABC Radio Melbourne.

The emerging outbreak has prompted a move to limit home gatherings to five visitors per day and public gatherings to 30 people from 6pm on Tuesday.

Masks are now also mandatory indoors for people aged 12 and over, though they can be taken off for eating, drinking and exercise.

Schools and workplaces will remain open, as will shops, cafes, restaurants and pubs, however existing density limits apply.

The new restrictions apply only to Greater Melbourne, or people travelling into regional Victoria, and will be in place until at least June 4.

But visitor restrictions will also be introduced at hospitals and aged care facilities across the state.

"This is about giving our contact tracers the time that they need to track this matter down and get on top of it," Acting Premier James Merlino told reporters.

He said a public health advisory panel would weigh up if further restrictions would be required for large events including football matches.

It comes as AFL club Western Bulldogs has been plunged into isolation after an employee visited Highpoint Shopping Centre during the exposure times.

The Western Bulldogs expect their players and staff to return to training on Wednesday, pending negative test results being received overnight.

More "tier one" exposures sites were identified on Tuesday afternoon including a McDonald's at Clifton Hill and a CBD restaurant.

Queensland, Western Australia and the other states have tightened their borders with Victoria while stopping short of completely slamming them shut.

All Victorian arrivals to WA now need to take a test and isolate until they receive a negative result, while those arriving into Queensland from the Whittlesea area must enter hotel quarantine from 1am on Wednesday.

"We'll monitor what's happened in Victoria over coming hours and days and see if we need to toughen the arrangement," WA Premier Mark McGowan said.

"Or indeed, if they get it under control, there are no further cases, we may be able to soften the arrangement."

Earlier, Mr Merlino said the man in his 60s may have been infectious for 10 days, suggesting he could be the possible "source case" for the City of Whittlesea outbreak.

Genomic sequencing shows the outbreak is linked to the case of a Wollert man, who contracted the virus in South Australian quarantine earlier this month.

Wollert falls within the City of Whittlesea, and the man shopped at the same Woolworths in Epping North as one of the new cases, albeit on a different day.

Professor Sutton, however, said authorities were yet to establish a "definitive link" between the Wollert man and the nine cases.

Meanwhile, the operating hours of some 26 testing sites will be expanded, including the Melbourne Showgrounds, which reached capacity after being open for five minutes this morning.

Authorities also urged "millions" of eligible Victorians to get vaccinated and "avoid restrictions".

Mr Merlino flagged he would make an announcement about expanding the vaccine eligibility criteria in Victoria in the "coming days".

Australian Associated Press