But National's spokesman for the Covid-19 response, Chris Bishop, pointed out on Twitter that the Covid-19 Public Health Response Act 2020 actually said people can drive to get to a suitable exercise spot in level 4.
The Police say you can’t drive somewhere for exercising. This is not what the COVID-19 Public Health Response (Alert Level Requirements) Order (No 9) 2021 says. pic.twitter.com/cSV1wpJGyc
Police have amended the post, and a police spokeswoman said they were not aware of anyone being incorrectly warned or charged.
Covid-19 Response Minister Chris Hipkins confirmed in Sunday's 1pm press conference that it was acceptable to drive to a nearby spot for exercise "if they can't exercise right beside their home within walking distance".
"But they shouldn't be travelling miles to go to the beach or to somewhere that's a long way away."
For example, people who lived on a hill and were elderly or had young children could drive somewhere flat to get their exercise.
People in a built-up area who couldn't socially distance while exercising could drive somewhere safer.
"But we don't want people travelling across town - so it should be to ... the nearest place that you can go."
Bishop also shared on Twitter a letter that had been placed on a vehicle's windscreen, saying the person was breaching level 4 rules by using their vehicle for non-essential reasons.
This could help spread the Delta variant of Covid-19 and also put emergency services at risk if the person had a crash, the letter said.
"You are to return to your isolation address immediately. Your vehicle details have been recorded by police," it said.
Police confirmed the notice was authentic and had been placed on windscreens of vehicles in remote places around Wanaka, to deter people from undertaking "potentially dangerous activities such as tramping or hiking".
Senior Sergeant John Fookes, Otago Lakes' central area prevention manager, said there had been "persistent problems with people travelling to areas outside of their neighbourhood to exercise or undertake recreational activity, such as tramping, hiking, mountain biking and even jet boating".
"We saw this during last year's level 4 restrictions and again during this current lockdown. We remind the public that these activities fall outside the permitted activities under the restrictions of alert level 4, and the potential for injury means emergency services are exposed to risk when they have to rescue people.