The woman, also known as Posie Parker, had been scheduled to visit the country next week.
Earlier this year, her Let Women Speak tour came to an abrupt end after thousands of trans-solidarity protesters showed up.
In a video on social media, Keen said even if officials allowed her into New Zealand, she felt police would not protect her or her supporters.
"I don't trust that the police are going to come and look after me, or any women attending."
She then went on to accuse the country's police, border forces and politicians of corruption.
Inspector Richard Sami said today police were aware of the potential for significant protest activity in central Auckland surrounding a planned hearing in the Auckland District Court next week.
"Our staff have been speaking with representatives of Ms Keen-Minshull to understand their plans and convey advice regarding personal safety.
"Planning is well advanced and we are well connected with other agencies in regards to this matter, including the Ministry of Justice."
Police would be present to monitor and minimise disruption to the wider public, Sami said.
"Police recognise the lawful right to protest, and our role in these situations is to uphold the law and ensure the safety of all."
Customs have been approached for comment.
