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A video has been circulated on various right-wing websites, including one run by Cameron Slater, which shows Wiles and another woman sitting on an Auckland beach talking without masks.
The video also shows the other woman at one point swimming briefly in the calm water as Wiles watches.
In various posts, Wiles is accused of breaking level 4 lockdown rules.
Wiles told the Herald this was not true.
The friend was living alone so had joined Wiles' bubble.
They had gone for a bike ride in their local area, which is permitted, and as they were outside away from others had taken off their masks to chat on the beach - also permitted.
"We all know that alert level 4 is hard, especially for those who live alone. A good friend of mine lives alone and was struggling a bit so I invited her to join my bubble."
The two regularly cycle together anyway, and so continued through lockdown.
On the day of the video they cycled to Judges Bay and on the "near-deserted beach", took off their masks and "had a chinwag".
Wiles said she did accept her friend had broken the rules by swimming.
"It is clear my bubble mate did break the rules by going for a swim. She shouldn't have done it, and I should have stopped her, but I am not her mum. It is, though, important people do stick to the rules."
On Friday, director general of health Dr Ashley Bloomfield clarified it was okay under alert level 4 to cycle 5km from someone's home with someone from their bubble and not be wearing a mask.
"The Prime Minister has earlier talked about, if you are keeping well away from other people and you're undertaking exercise on the more vigorous side, yes that is fine."
Bloomfield said he had been contacted by Wiles about the video, and after explaining her actions to him he agreed there were no rules broken by her.
Deputy Prime Minister Grant Robertson said he had not seen the video but that "everyone should follow the rules".
Wiles said it was "disappointing" to have mistruths spread about her, but it was understanding people were feeling on edge at the moment.
"It is looking really good [for Auckland] and we are at that point where the cases are coming down and everyone has been doing their best. But we are just not quite there yet and everyone's nerves are fraying a bit."
During the first lockdown last year, then-Health Minister David Clark stepped down after it was revealed he drove 2.3km in his work van to go mountain biking in Dunedin.