American anti-vaccination campaigner Dr Sherri Tenpenny has cancelled her speaking tour of Australia amid security concerns.

The controversial speaker had booked appearances in Brisbane, Sydney, Adelaide, Melbourne and Gold Coast, however a number of venues had cancelled because of mounting complaints from the public.

In a statement posted on Facebook, Dr Tenpenny said that "pro-vaccine extremists had made continual, anonymous threats of vandalism and violence" and that organisers could no longer guarantee the safety of attendees.

Fellow anti-vaccination campaigner Australian Stephanie Messenger had been due to speak with Dr Tenpenny and had organised much of the tour.

"Some people were planning to bring babies," she said in the Facebook statement.

"The threats have been persistent.

"We are not able to insure that the attendees would be safe from harm."

Ms Messenger also claimed that "pro-vaccine extremists have been sabotaging the venues and have threatened to disrupt the normal business operations of the locations during the meetings".

The tour organisers said additional options for Dr Tenpenny were being considered but were not confirmed at this time.

They said that refunds would be issued for all tickets sold.

Police in several states said they were investigating the threats, but said there was evidence the threats may have come from Australian anti-vaccination activists.

Dr Tenpenny said she has also cancelled her planned vacation in Australia.

Virologist and pro-vaccine campaigner Dr David Hawkes said the cancellation of the tour was a win for people who were concerned about public health.

"This hasn't been driven by medical professionals and politicians," he said.

"It's been driven by parents generally at a community level who were concerned about the emergence of diseases like whooping cough in the last few years due to less than ideal vaccination rates."