At least five venues have cancelled events featuring a controversial US anti-vaccination campaigner, amid a growing internet protest against her visit.

At least five venues have bowed to public pressure and cancelled events featuring a controversial US anti-vaccination campaigner.

Osteopath Sherri Tenpenny was due to deliver anti-vaccination messages at 11 venues on the east coast in February and March, with some tickets to seminars and dinners selling for as much as $200.

Dennis Skinner, manager of the Kareela Golf and Social Club in southern Sydney, said he cancelled Dr Tenpenny's appearance after being inundated with protest emails and Facebook messages.

"We don't have a position for or against (vaccination)," he told AAP on Thursday.

"We just decided that it was so controversial we decided to back away from it."

Four other venues in Sydney and Melbourne had cancelled arrangements by Thursday afternoon, according to event listings on the website Eventbrite.

"The organiser has cancelled our booking due to bullying by vested interests who do not believe in informed consent, free speech, and respect for other's (sic) rights," a message on the website reads.

The cancellations come as a change.org petition calling on the government to refuse Dr Tenpenny a visa approaches 6000 signatures.

Immigration Minister Peter Dutton was taking advice on the matter, a spokesman said.

A move to ban a controversial speaker has a recent precedent.

Julien Blanc, a self-described "pick-up artist", had his visa cancelled in November following an online outcry over seminars advocating cruelty to women.

Dr Caroline West, a senior philosophy lecturer at the University of Sydney, said free speech should be restricted if it could cause harm.

"The overwhelming evidence seems to be in favour of vaccination and the overwhelming majority of experts agree that it's the right thing to do," she said.

"If we've got good reason to think it will be harmful to allow misinformation to be spread, it seems like there is a pretty strong case for restricting free speech in this instance."

But the head of Civil Liberties Australia, Tim Vines, said denying Dr Tenpenny the right to speak would set a dangerous precedent, even if her ideas were unscientific.

"They might be wrong, but they are still entitled to voice that opinion," he said.

Dr Tenpenny is at the vanguard of a movement that believes vaccines are associated with a variety of diseases, including autism and asthma.

Brian Moreton, chairman of the Australian Medical Association's council of general practice, said anti-vaccination messages posed a significant public health risk.

"The danger is that people who don't have access to the correct information will believe the nonsense spoken by the anti-vaccination movement and vaccination rates will fall," Dr Moreton said.

He said the AMA supported free speech and stood behind the considerable evidence in favour of vaccination.

Organisers of Dr Tenpenny's tour have been contacted for comment.