Paula Bennett says she will not be put off making public appearances despite an online threat which said someone should "shoot the b**** dead" at her next public outing.
The Social Housing Minister said this morning that she referred all violent threats to the police.
In a Facebook post two weeks ago, a user wrote: "People own guns out there I dare any[one] to shoot the b**** dead at [her] next public appearance.
The person added: "Gosh I hope keys is standing beside her, 2 birds 1 bullet."
Speaking to reporters at Parliament this morning, Mrs Bennett said violent threats affected her family more than her.
"When you've got your own kids pointing out on social media that someone should shoot me at my next public event it's pretty distressing..."
She did not think she was being targeted, despite a series of incidents in the last few weeks.
At a visit to Whanganui last week protesters had been "aggressive" and police had been called in as a result.
"They had sex toys with my name on them and that sort of thing. So the whole thing was a bit unsavoury, to be fair."
She was told by a commenter on Facebook page last week that "a bit of sexual violence never hurt anyone" after she took a strong stance against campervan company Wicked Campers.
Mrs Bennett said she hoped that ministers would not require a greater police presence as a result of the threats.
"I want to remain a good Kiwi woman and be able to go to the supermarket and be able to take my kids to the park," she said.
"I want to be able to live my life ... as normally as I possibly can."
She had reported around 12 incidents to police. A small group of people were responsible for the offensive threats, she said.
Labour leader Andrew Little said the threats against ministers were "ugly" and "had no place" in New Zealand's political debate.
It was "hard to gauge" whether treatment of MPs was getting worse, he said. But he had observed a "palpable sense of anger" from voters which was not present a year ago.
"I think there is a lot of frustration and anger. People see a Government that looks increasingly arrogant, it's smug and out of touch... and they are feeling frustrated."
A University of Otago research paper released last year showed that nine out of 10 MPs had been victims of harassment, some of it violent.