Ms Keen-Minshull's radical "Let Women Speak" tour has scheduled events in Auckland and Wellington on Saturday and Sunday.
While UK nationals are usually able to enter New Zealand without a visa, Immigration New Zealand (INZ) is investigating Ms Keen-Minshull's application ahead of those events.
"INZ is now reviewing whether in the light of the events at the weekend Ms Keen-Minshull is still able to travel to New Zealand ... without obtaining a visa first," INZ general manager Richard Owen said.
Under New Zealand's immigration rules, either INZ or Immigration Minister Michael Wood can intervene and cancel a visa.
However, such actions are usually taken based on a person's criminal background, meaning an assessment of how the Melbourne incident might weigh on Ms Keen-Minshull's application is outside of the usual parameters.
Last year, far-right Australian blogger Avi Yemini was denied entry to New Zealand due to a criminal conviction.
Mr Yemini had sought to enter New Zealand to visit the occupation of parliament grounds by anti-vaccine and anti-mandate groups.
Ms Keen-Minshull travels the world campaigning against the recognition of transgender women.
The rally in Melbourne on Saturday has sparked concern in New Zealand, particularly among the trans community, who fear a repeat of the harrowing scenes.
Prime Minister Chris Hipkins would not be drawn on the likelihood of Ms Keen-Minshull's arrival, saying "there's a process that is being worked through".
He said he did not support the protest.
"I condemn people who use their rights to free speech to do that in a way that seeks to deliberately create division," he said.
"It's not something that I would attend or would engage with.
"I don't think it's helpful overall to social cohesion or ... rational and constructive debate.
"We don't want to incite hateful behaviour or violence. In fact, it's illegal to do so."
A police spokesman said officers "will be present to monitor and respond to any issues that may arise, and to minimise disruption to the wider public".
The Wellington event is planned for Civic Square, an outdoor space managed by the council.
Mayor Tory Whanau said she "strongly condemned the views and actions of this group" but conceded she could not stop an event on public land.
"I acknowledge that freedom of expression, movement and peaceful assembly are rights preserved in the New Zealand Bill of Rights Act 1990," she said.
"This protest is against principles Wellingtonians, and me personally, hold dear."
A local group sympathetic to Ms Keen-Minshull's views, Speak Up For Women NZ, admonished the involvement of neo-Nazis in the Melbourne rally.
"We are opposed to Nazis in every way and do not wish for them to attend," the group posted on Twitter.
"They will not be welcome. We are a non-partisan women's rights group and we simply wish to attend."
