"I have some concerns with the way we have shown leadership around Covid as a council," she said.
Wensley believes the markets are "building a brand" on "flouting the rules".
Under alert level red, outdoor farmers markets and occasional markets with retail stalls only, may open with capacity limits, with face masks worn by staff and customers.
Videos posted to the Free Marketeer's Facebook page show a large number of unmasked visitors and stallholders.
Wensley accused the market of not adhering to red level precautions by hosting areas to sit and eat.
In red level, advice from the Ministry of Business, Innovation and Employment, is if food is to be consumed on-site under the control of the business (including outdoor areas), then the business must follow food and drink service regulations. This means at all levels, food and drink providers would have to be vaccinated unless the work is solely for takeaway food and drink.
Council staff member Dennis Bush King said it was not the task of Tasman District Council staff to enforce rules around eating.
TDC chief executive Janine Dowding said she believed WorkSafe were responsible for managing compliance.
In a statement, Nelson MP Rachel Boyack said she has been contacted by a number of people who are concerned with the Richmond showgrounds market and that she has passed those concerns onto WorkSafe.
"WorkSafe have assured me that they are investigating the concerns and reports raised with them, and that they take them seriously."
WorkSafe was unable to say at this stage how many complaints they had received to do with the Richmond market.
A WorkSafe spokesperson said the agency had visited the Nelson Free Marketeers market, where inspectors identified areas of "non-compliance" and were considering their follow-up actions.
Regulations chair Dana Wensley said a letter was sent on behalf of the committee to WorkSafe last Friday in the interest of further "clarity and consistency".
"The essence of the letter was that council is pursuing regulatory responses to the freedom markets at Riwaka, and we are requesting that WorkSafe pursue what we consider to be 'flagrant breaches' of Covid workplace regulations in relation to the markets held at the Richmond A&P show grounds."
Nelson Free Marketeers manager Penny Cameron refused to comment on the markets to Local Democracy Reporting, stating they had seen "nothing but lies from the media".