Three were aged in their 90s and three in their 80s.
Twenty-two people have died in the past seven days.
Australia has recorded 13,132 cases of coronavirus so far: 3444 in New South Wales, 1073 in Queensland, 7142 in Victoria, 447 in South Australia, 654 in Western Australia, 227 in Tasmania, 113 in the ACT and 32 in the Northern Territory.
Andrews said 206 Victorians are in hospital, 41 of those are receiving intensive care.
Some 2240 cases of coronavirus have been recorded in Victoria since last Friday.
Andrews said there were issues with people who test positive not answering their phones to authorities.
Premier of Victoria Daniel Andrews wearing a mask arrives for a press conference. Photo / Getty Images
He said that, from today, if those people don't answer a second phone call, the Australian Defence Force will knock on their door.
"It goes without saying though, if you were door knocked and you were not found at home, then you are in breach of the orders because you are a positive case and you should be at home," he said.
"So that would almost certainly lead to you being fined. So that is not the purpose of this but if ADF, an authorised officer visit you and you are not at home.
"They will continue to visit you but you will have some very clear explaining to do as to why you are not at home isolated because you have tested positive."
He praised Melburnians for wearing masks, insisting they are working in slowing the spread.
"I am encouraged to see so many people across Melbourne wearing masks," he said.
"You want to thank you for that stop you know it is not always easy but it is a very important way.
"Medical advice tells us we are in a different phase then we were the first time. These circumstances are different and masks can play and are playing a really big part in slowing this down.
"I want to thank all of those who are coming forward to getting tested, all of those who are following the rules and only going out of their home for those four permitted reasons when they need to end only for the things they need.
"People are making many sacrifices and I am grateful to all of you."
Victorian Police Minister Lisa Neville said 101 fines had been handed out to Victorians for breaking virus rules in the past 24 hours.
Some were for people not wearing masks.
"They are people deciding they still want to party, people who have decided they want to continue to go to brothels, decided that the gym can continue to operate and of course people who have decided to go into unrestricted areas," she said.
She said police had been handing out face masks to people without them but had still issued some $200 on-the-spot fines for non-compliance, in the first 24 hours of the mandatory mask rule.
Prime Minister Scott Morrison told media the 300 cases, opposed to the 400-plus cases the state has been seeing regularly over the past week, was "better news".
"While there is some better news today out of Victoria, that is not something that we can assume will continue.
"And so we must maintain the full force of effort in Victoria. In New South Wales, the news is better.
Australian Prime Minister Scott Morrison. Photo / Getty Images
"I think what this demonstrates is that we're in this fight and in some fights, we'll be behind and in some fights we'll be ahead. But we're always in the fight in Australia.
"And what it demonstrates is that you can deal with outbreaks, you can get on top of them.
"But you've got to be constant about it and you've got to throw everything at it. And we will get on top of it in Victoria because there is the determination and the cooperation to achieve that and that was reinforced today."
Victoria could face up to two years in isolation from the rest of the country if it doesn't bring its Covid-19 outbreak under control, one epidemiologist has warned.
Speaking to the ABC on Wednesday, Professor Tony Blakely said Australia was facing a "real dilemma" with the current coronavirus situation.
He said six out of eight territories had achieved elimination "by accident", meaning they might not open their borders to Victoria or NSW residents until the latter states could achieve the same.
"Why would they let anybody in if there's enough of a risk that they are going to bring the virus?" Blakely said.
"So let's assume that Victoria doesn't get rid of the virus ... It essentially means Victoria is going to have to function in isolation from the rest of Australia until such time as we get a vaccine, assuming the other states don't want the virus back in. If I was in the [other] states, I wouldn't want the virus back in."
While many countries are racing to develop a vaccine, it could be years before one is available to the public.
Blakely said if Victoria doesn't pursue an elimination strategy, the only other option was forcing the other states to "let the virus back in and we move to the yo-yo common denominator".
He said introducing a hard lockdown in Victoria would be for one of two reasons.
"One is that you are actually going for elimination, which I'm still advocating for because that's the better strategy in the medium to long term, 18 months, two years, it would be better to be in that state," he said.
"The other reason is that if the ICU capacity or health services were under threat. We are not at that level yet; it would be 2500 cases a day before ICU would be near to that number. It's not being used in Victoria yet."
NSW
In New South Wales, new coronavirus restrictions apply to cafes, restaurants and clubs, and weddings and funerals from today.
Weddings and corporate events will be able to accommodate fewer people, with a limit of 150. Guests will have to be seated, and no dancing or mingling is allowed. Funerals and religious venues will be allowed a maximum of 100 attendees.
