The 51-year-old former Black Caps captain collapsed in Canberra two weeks ago, having suffered a massive heart attack - resulting in an aortic dissection, a tear in the inner layer of the body's main artery.
He was rushed to a Sydney hospital for emergency heart surgery last week and has been on life support since.
According to a statement on Friday, Cairns and his family "are thankful for all of the support and well wishes from everyone, and for the privacy they have been afforded".
Cairns, the son of Black Cap legend Lance Cairns, was a right-hand batsman and fast-medium bowler. He was known as one of the finest all-rounders of his generation.
He has been living and working in Canberra with his wife Melanie and their children for several years.
Cairns had to rebuild his life after walking out of Southwark Crown Court in London in 2015 after being found not guilty of perjury and perverting the course of justice charges in relation to match-fixing allegations.
