Rhonda Stuart, the head of infection control at Monash Health, was the first recipient of the COVID-19 vaccine in the state shortly after 7:30am on Monday.

"I'm really proud to be getting this vaccine and starting the next chapter in our work against COVID," she told reporters.

"Now the aim is to get all our healthcare workers vaccinated and then out to the public as well."

Professor Stuart's team treated the first Australian case of COVID-19 in January 2020, a returned traveller from Wuhan in China, as well as hundreds of others since.

"(It's) so amazing we've got to this stage where we can be vaccinating people," she said.

Frontline workers in healthcare, aged care and hotel quarantine will be among the first to get the jab at dedicated vaccination hubs at Austin Health, Monash Health and Western Health hospitals.

The federal government has allocated about 12,000 doses to Victoria in the first week of the rollout, with up to 59,000 doses expected in the first four weeks.

Six other public hospitals will also become vaccination hubs as more doses become available, while mobile units will visit aged care residents and people living in disability care.

Nurse Rachel Hogben, who manages the intensive care unit at Dandenong Hospital, said she felt relieved to receive the jab.

"I'm actually a little bit more emotional than I thought that I would be," she said.

"I feel like this is the way forward ... we're no longer acting defensively against this, we're now on the offensive and it's an amazing day."

Among the first to be vaccinated at Austin Health were nurse Grace Gibney, who manages the hospital's COVID-19 screening clinic, and Chris Quinn, a registered mental health nurse working in hotel quarantine.

Health Minister Martin Foley described the duo as the "real heroes of the past 12 months".

"It's only appropriate that those people who put the most on the line get first in line when it comes to the vaccine program," he said.

"It was a really exciting moment for them and their colleagues to start this process."

Infectious diseases expert Ben Cowie, who is advising the Victorian government on the vaccine rollout, said the Pfizer and AstraZeneca vaccines were "safe, effective and free".

"They've been tested initially in clinical trials which involve tens of thousands of individuals and have subsequently been administered to tens of millions of people worldwide," he said.

It comes after the trophy presentation at the men's Australian Open final on Sunday was marred by members of the crowd, who booed when the coronavirus vaccine rollout and Victorian government were mentioned.

"I'm certainly cheering the start of the vaccination and I think there's probably a lot more people at home who are cheering than booing," Professor Cowie said.

"It's totally understandable that many Victorians have questions about the vaccines and about the program, and I'd encourage people to express those questions and their viewpoints in a peaceful and respectful way."

Opposition spokesman David Davis said while he "strongly supported" the vaccine rollout, he understood why people booed the state government.

"If I were at the tennis I would have booed when Daniel Andrews was mentioned too," he said.

Victoria recorded a third consecutive day with no local cases of COVID-19 on Monday following 8277 tests.

Two indeterminate test results were received on Sunday for hotel quarantine workers at the Novotel and Pullman hotels, but subsequent tests came back negative.

There are 25 active cases across the state.

Australian Associated Press