It follows months of speculation over whether Brown would be granted visas because of his domestic violence conviction.
The statement from promoter Ticketek did not give a reason for the cancellation.
It said Brown was "positive" the One Hell of a Nite tour, due to start next week, would take place at a later date.
"Mr Brown wishes to express his deepest gratitude to the fans for their support and looks forward to a successful tour in the near future," the statement said.
An Australian Immigration Department spokesperson told the BBC it could not comment on the case.
"For reason of privacy the department cannot discuss any material provided to the minister by either Mr Brown or representative," the spokesperson said.
A New Zealand immigration spokesperson reportedly said Chris Brown had withdrawn his work visa application for that country, and no decision had been made on the application.
Brown pleaded guilty in 2009 to assaulting his then-girlfriend, pop star Rihanna. He has since toured Australia twice.
But in September, Australia's immigration department issued a "notice of intention to consider refusal" ahead of his next planned tour.
Minister for Women Michaelia Cash, a former assistant immigration minister, had urged Immigration Minister Peter Dutton to take a stand on the issue.
Brown later said he wanted to go to Australia to use his influence as an entertainer to "raise awareness about domestic violence".
"My life mistakes should be a wake up call for everyone," he tweeted in September.  "Showing the world that mistakes don't define you. Trying to prevent spousal abuse."
Earlier this year, Australia refused a visa to world champion boxer Floyd Mayweather on similar grounds.
The 37-year-old American has a criminal record, which includes serving two months in jail in 2012, after pleading guilty to an assault on his former partner in front of their children.
Mayweather had been booked for dinner and nightclub appearances in Sydney and Melbourne in January.
US singer Chris Brown's tour of Australia and New Zealand has been cancelled, promoters have confirmed.