In a statement posted to social media Mikakos said she had written to Victoria's Governor to resign as minister, and will also be resigning from the Parliament.
But she defended her handling of the pandemic, and said she disagreed with parts of Andrews' statement to the inquiry.
"I have never wanted to leave a job unfinished," she said.
"But in light of the Premier's statement to the board of inquiry and the fact that there are elements in it that I strongly disagree with, I believe that I cannot continue to serve in this Cabinet."
Victoria's hotel quarantine inquiry was launched after it emerged that the state's second wave was fuelled by Covid-19 jumping from guests in the programme to workers, then spreading through the community.
Genomic sequencing data in July showed more than 99 percent of Victoria's coronavirus cases could be traced back to returned travellers.
Yesterday the Premier told the inquiry that he viewed Mikakos as accountable for the programme, but said he did not know who decided to use private security contractors to guard guests' rooms.
Not one person who gave evidence to the inquiry was able to say who made that decision.
Mikakos said she took responsibility for the department, but said the hotel quarantine programme was not her responsibility alone.
"I am deeply sorry for the situation that Victorians find themselves in," she said. "In good conscience, I do not believe that my actions led to them."