Cairns, 51, was on life support after having cardiovascular surgery in Australia's capital city.
His family have said he has had further heart surgery at St Vincent's Hospital in Sydney.
A statement from his wife Melanie also thanked "everyone for their warm wishes, prayers and kind words".
Considered one of the best all-rounders of his generation, Cairns played 62 Tests, 215 one-day internationals and two Twenty20 matches for New Zealand between 1989 and 2006 before becoming a television pundit.
His father Lance also represented the New Zealand cricket team.
"We're deeply concerned to hear of Chris Cairns' medical emergency," said New Zealand Cricket chief executive David White.
"Our thoughts are with his family in Australia and here in New Zealand. Chris is a much-loved husband, father, and son - and remains one of our finest all-rounders. We hope he's able to make a full recovery."
After retiring from international cricket, Cairns was the subject of allegations of match-fixing in India as captain of the Chandigarh Lions in the defunct Indian Cricket League in 2008.
He denied any wrongdoing and fought several legal battles to clear his name, winning a libel case against former Indian Premier League chairman Lalit Modi in 2012.
In 2015, he was cleared of perjury and perverting the course of justice at Southwark Crown Court.