The state recorded 71 local COVID-19 cases on Monday, of which 55 were not isolating when they should have been.

Forty-nine of the new cases are linked to known outbreaks, but the sources of 22 infections are a mystery.

Premier Daniel Andrews on Monday revealed a small number of people infected with COVID-19 had "taken a few extra days" to get tested.

"This thing moves so fast that even a few extra days almost guarantees that you will give it to multiple other people - your family, the people you love the most - and you don't want that," he told reporters on Monday.

Mr Andrews said some close contacts of positive cases were not self-isolating for the required 14 days.

"If you're asked to isolate, it is incredibly important that you do that," he said.

"There's no ducking down the shops or going and visiting someone. There's no room for error."

COVID-19 Commander Jeroen Weimar said while some cases were asymptomatic, others were seriously ill prior to testing positive.

"We've seen examples of children collapsing at school and vomiting at school, that's how ill they are," he said.

"When we then go to (the child's) household we realise it's not just one person positive, there are a number of people in the house who are positive, there are a range of symptoms being displayed."

Mr Weimar also appealed to young men in Newport, west of Melbourne, to get tested after 10 more cases were connected to that cluster, noting there are payments of $400 for casual workers required to get tested and $1500 for those required to self-isolate for 14 days.

Among the new cases are five staff and patients at the Royal Melbourne Hospital, where an infected Shepparton man had surgery on August 12.

He was not tested for COVID-19 before being admitted and had been in various parts of the hospital, including the intensive care unit and a cardiac ward.

The hospital confirmed a total of four patients and six staff have tested positive for COVID-19, while 450 health workers have been furloughed and required to isolate until further notice.

The 22 mystery infections live across Melbourne, including in Camberwell, Essendon West, Fitzroy North, Maidstone, Sorrento and Thornbury, and bring the total number of active cases in the state to 494.

Twenty-nine Victorians are battling the virus in hospital, including nine in intensive care, five of whom are on ventilators.

As of Monday morning, there were more than 52,000 vaccine appointments available for the week ahead, with Mr Andrews imploring Victorians to fill them as the state aims for one million doses by mid-September.

He said there have been 10,000 cancellations and no shows each day, possibly due to widened Pfizer eligibility from next month.

"An appointment today is better than a booking in a fortnight or a month," Mr Andrews said.

He also condemned a violent anti-lockdown protest held on Saturday, describing those who attended as "shameful" and "disgusting".

Victoria Police Chief Commission Shane Patton has described the protest as one of the most violent the city has seen decades, with 21 officers injured, including one who may need surgery.

Australian Associated Press