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.
Last week Mrs Bennett was in a car with National MP Chester Borrows at the time of an incident involving protesters.
She said it was an "unnerving" experience because the protesters had been acting aggressively earlier in the day.
"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."
The minister said she did not feel targeted despite recent abuse, which included highly offensive threats on social media after she took a hard stance against campervan company Wicked Campers last week.
National MP Chester Borrows says police have not spoken to him about an incident last week in which he appeared to drive his car into protesters.
Mr Borrows this morning stood by his actions last Tuesday, which left one protester, Tracy Treadwell, with a minor leg injury.
"I'm happy with the way that I responded to what was in front of me at the time and what we knew at the time," he said.
"I'm glad that the lady's not hurt. Everyone's got a right to demonstrate. I've done that myself in the past."
Police said on Thursday they were aware of the incident, confirming one person was injured.
Social Housing Minister Paula Bennett was in Mr Borrows' car at the time
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.
