The latest Victorian death from the coronavirus was that of a man aged in his 80s who died in a Melbourne hospital.
More than 39,000 tests for the virus have now been conducted in the state, with 21 confirmed cases of community transmission and 93 people who have recovered from the illness.
Ms Mikakos said 26 people were in hospital being treated for the disease. Four of those were in intensive care.
The minister said the state was performing about 4400 tests each day, with 11, mostly private, labs joining the effort. That testing capacity was expected to grow in the coming days, she said.
Strict quarantine regulations forcing international arrivals to spend 14 days in a hotel began at midnight on Saturday.
About 470 returned travellers were due to fly into Melbourne Airport on seven flights on Sunday. They will be housed in hotels around the city.
Ms Mikakos said the process had gone smoothly from the first of several flights to arrive under the tough new regime.
She condemned the “stupid behaviour” of those Victorians who went to beaches at the weekend, saying they had put lives at risk through their conduct.
“I share the frustration of my Chief Health Officer,” Ms Mikakos said, echoing Dr Brett Sutton’s comments on Saturday criticising people’s “crap” behaviour.
“It is, it is stupid behaviour,” Ms Mikakos said.
“We all need to do our bit, so it’s just those small minority of people who are putting the rest of the community at risk. We all need to make some sacrifices here.”
The minister said the latest number of positive tests was worrying and the social-distancing rules were the only way Victoria could avoid being overwhelmed by the pandemic.
“The numbers do continue to trend up and that is very, very concerning to us,” she said.
“If you can stay at home, you must stay at home.
“This is the only way we’re going to defeat COVID-19 It’s the only way we’re going to slow down the spread of COVID-19.”
Ms Mikakos acknowledged that it had been difficult for the public to keep up with the social-distancing rules in what she called an “evolving situation” and promised more government advertising with clear and simple guidelines.
“I acknowledge that the rules have have evolved over time and that is because national cabinet has been responding to an evolving situation,” the minister said.
“So we want to make it as easy for people to understand as possible, and so there will be more advertising that will be coming … and making the rules very clear to people.”
Noel Towell is State Political Editor for The Age