The self-prescribed "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."

Labor's health spokeswoman Catherine King, who wrote to Mr Dutton to try and stop Heckenlively from coming to Australia, applauded the decision.

She said it was important to deny entry to someone who thumbs their nose at science and wants to spread "very dangerous information" that has a very serious public health impact.

"On the public interest grounds, there are some messages that are just not worth the risk of having them spread widely out in the community," Ms King told ABC radio.

"We've already got problems in this area, we don't need this person contributing to them."