Premier Daniel Andrews has appointed Martin Foley to the state's health portfolio following Jenny Mikakos' resignation and has rejected the idea he should go too.
Grilled by journalists on Saturday afternoon following the health minister's announcement hours earlier, Mr Andrews said he did not ask Ms Mikakos to go but thought it an "appropriate course of action".
He would not be drawn on why, deferring to the findings yet to come out of the hotel quarantine inquiry.
The premier and key ministers have been in hot water since it emerged that the use of private security guards, instead of police or military, led to breaches causing the state's second COVID-19 wave, which prolonged lockdowns and economic stress across the country.
In a statement on Saturday morning, Ms Mikakos said the premier's comments about her and her department's responsibility for the running of hotel quarantine meant she could not continue to serve in his cabinet.
"I am disappointed that my integrity has sought to be undermined," she wrote.
Ms Mikakos also intends to resign from parliament.
The premier said Ms Mikakos was "a very, very hard working person and I'm grateful to her for her efforts".
He was informed of her decision to resign and then received a direct text message from her.
Asked on Saturday if he too should quit, Mr Andrews answered "no" and that his government was unified with a "singular focus" to defeat the pandemic.
"I don't run from challenges," he said.
Incoming health minister Martin Foley has experience with the Department of Health and Human Services through his mental health portfolio and wa to be sworn into the role on Saturday afternoon.
Victoria's daily cases again continued in a promising downwards trend with just 12 new infections recorded on Saturday.
One further death of woman in her 80s linked to aged care, brings the state toll to 782.
There are 444 active cases remaining in Victoria, of which just 10 are in regional areas.
Ms Mikakos said in her resignation letter that when case numbers in Melbourne started to rise again in June, she sought an explanation and received a briefing on a genomic sequencing report.
It confirmed 99 per cent of Victoria's second wave infections could be linked to outbreaks among staff and security guards at the Rydges on Swanston and Stamford Plaza hotel.
"To say that I was shocked would be a massive understatement," she said.
While she took responsibility for her department she also took aim at DHHS for not briefing her on some issues.
This reflected her evidence at the inquiry that she was "very disappointed" problems identified with the program early on were not raised with her.
While Ms Mikakos apologised for the "situation" Victorians were in, she said she did not believe her actions led to them.
The Victorian opposition welcomed her resignation and called on the premier to resign.
"Victorians have been given nothing but finger pointing and cover-up," opposition leader Michael O'Brien said.
Meanwhile, Melburnians are waiting for the easing of restrictions on Monday after the city's 14-day case average fell again on Saturday to 23.6. The average is only 0.8 in regional Victoria.
The premier will make announcements on Sunday about the easing of lockdowns, though he has tried to temper expectations that go beyond the "roadmap" unveiled several weeks ago.
The state opposition wants an expansion of the easing of restrictions, such as abolishment of the 9pm curfew in Melbourne, the return to school for all students, and reopening of restaurants, retail businesses and offices.
Planned changes from Monday are significantly more conservative, with a staged return to school for some students, the return of childcare and permission for outdoor gatherings of five people from two households.
Australian Associated Press