Ms Mikakos dramatically resigned as minister and from the upper house on Saturday after the premier told the hotel quarantine inquiry her department was ultimately responsible for the botched quarantine program.

The program failed because private security guards breached infection control, which allowed the virus to spread into the community, creating a devastating second wave.

Ms Mikakos blamed Mr Andrews' statement for her resignation in a scathing letter posted on Twitter.

"I have never wanted to leave a job unfinished but in the light of the Premier's statement to the Board of Inquiry and the fact that there are elements in that that I strongly disagree with, I believe I cannot continue to serve in his cabinet," she wrote on Saturday.

Mr Andrews has been conciliatory about Ms Mikakos since her resignation, which she informed him about via text message.

He again described her as "hard-working" without elaborating on her decision to quit on Sunday.

"When you make a decision that you can't serve in the cabinet then you can't serve in the government you know to tender your resignation and that's exactly what happened," the premier said.

"I wish her well, and acknowledge her hard work and her passion and her commitment."

Mental Health Minister Martin Foley was sworn in as health minister on Saturday, creating a cabinet vacancy with speculation that Ingrid Stitt will be nominated to fill it.

Mr Andrews said he wouldn't predict the choice of the Labor caucus, but described Ms Stitt as an "outstanding person".

"When I have announcements to make about that process having come to a conclusion, and I'll do that, and I'll also have some portfolio arrangments to make at that time," the premier said.

When asked if he would like to see a woman replace Ms Mikakos on the Legislative Council, he said that was also matter for caucus, but he's confident they would find someone suitable.

Australian Associated Press