Jacinda Ardern says she - and other Kiwis - are "very frustrated" with people flouting the rules of the level 4 lockdown.
To protect the country from the COVID-19 coronavirus, most businesses have been closed and people are required to stay home unless it's for nearby exercise and essential services.
However social media is being inundated with images of people refusing to follow the rules and stay in their bubble.
Their reaction has led to a public admonishment from the Prime Minister on Sunday.
"I have seen, as you will have, reports of New Zealanders not following the rules of the lockdown. This group we can all rightly feel very frustrated with," she said during her coronavirus stand-up.
"I spoke with the Police Commissioner this morning who has confirmed police have all the resources they need. That includes the power to arrest and detain if needs be.
"No one wants that. So I ask that people follow the rules in the same way that the majority of New Zealanders are."
Police have launched a new online form for people to use to dob in breaches of the lockdown. The form can be found at 105.police.govt.nz from Sunday.
Police Commissioner Mike Bush is urging New Zealanders to use the form instead of calling police with their reports.
"We know people want to do the right thing if they see others flouting the restrictions, but we want to ease the load on the non-emergency phone number," Bush said in a statement on Sunday.
"Police will take the information reported online and make contact to remind those breaching the restrictions of their responsibilities.
"We are continuing to take the approach of educating and informing people of their responsibilities in the first instance, but we will not hesitate to take enforcement action if people continue to ignore the restrictions."