The self-proclaimed "world's number one anti-vaxxer" has been denied entry to Australia.

The Turnbull government has been under pressure to block Kent Heckenlively from visiting Australia for a planned lecture tour in December.

Immigration Minister Peter Dutton described those entangled in the anti-vaxxer movement as dangerous people.

"Kent's not got any travel plans to Australia because we're not going to allow him to come here - we're not going to issue a visa for this particular individual," Mr Dutton told Sydney's 2GB radio on Thursday.

"We have been very clear in having a look right through this particular case, and it's clear to me that it's not in our national interest that he should come here."