The Somali-born author was to appear on Australian TV on Monday before starting her tour, titled "Hero of Heresy".
But she pulled out due to "a number of reasons including security concerns", event organiser Think Inc said.
Ms Hirsi Ali has faced death threats in the past.
"[She] hopes to be able to return to Australia in the not too distant future," Think Inc said in a statement.
About 2,000 tickets had been sold for the speaking events in Brisbane, Melbourne, Sydney and Auckland.
She was granted asylum in the Netherlands in 1992, and was elected as an MP in 2003.
Ms Hirsi Ali rose to international attention in 2004 as the writer of a controversial film on violence against Muslim women, Submission, after her collaborator, filmmaker Theo van Gogh, was murdered by a radical Islamist.
Having received repeated death threats over her challenges to Islam's treatment of women, Ms Hirsi Ali spent time living under 24-hour police guard.
She then moved to the United States, where she has maintained a high profile.
In an article for the Hoover Institution last month, Ms Hirsi Ali described what she called "political Islam" as being not just a religion but "a political ideology, a legal order, and in many ways also a military doctrine associated with the campaigns of the Prophet Muhammad".
Nearly 400 people had signed an online petition opposing Ms Hirsi Ali's visit to Australia and New Zealand.
"Against a backdrop of increasing global Islamophobia, Hirsi-Ali's divisive rhetoric simply serves to increase hostility and hatred towards Muslims," the petition said.
Protests had been planned at locations where she was speaking, and people who bought tickets were told their bags would be searched.
Think Inc said all ticketholders would receive refunds.
A former Dutch MP and prominent critic of conservative Islam, Ayaan Hirsi Ali, has cancelled a speaking tour of Australia and New Zealand citing security concerns.