Work and Income and Social Development Minister Paula Bennett have said that there is no policy which prevents a beneficiary buying sanitary items on the supermarket cards.
Only alcohol, tobacco and electronic appliances are specifically banned and it is up to
checkout operators to monitor those.
The allegation has ignited a storm on social media after blogger Tulia Thompson wrote about it and described it as "institutionalised sexism".
Ms Thompson said another woman tried to use a Winz supermarket card at the check-out at her local supermarket, and the card didn't work.
"The cashier called Winz to find out why the card wouldn't work, and found out it was because she had tampons amongst the items she was purchasing. She had to return them."
Ms Thompson said another woman had contacted her in response to the blog to say the same thing had happened to her at a supermarket and the reason her card was rejected was because her sanitary item had been incorrectly labelled in the supermarket system to "pull-ups".
Ms Thompson said clearly there needed to be better communication between supermarkets and Winz to ensure women were not embarrassed at the check-out counter.
A spokeswoman for the Ministry of Social Development said any claims that female hygiene products could not be purchased using the Work and Income payment card were "totally untrue".
"Individual items are not tagged on payment cards. If someone's card doesn't work, it would be for a system reason and not because of what the person bought.
"The only items banned from purchase on the payment cards are electronics, appliances, alcohol and cigarettes."
But the spokeswoman said if people had a specific case or example where they had been incorrectly advised by a case manager, please contact Work and Income so they could look into it.
Minister of Social Development Paula Bennett was not immediately available for comment but she posted on Twitter "Rumours that women can't buy tampons with Work and Income payment cards are simply not true.end of story."
The issue was also being discussed on Ms Bennett's FaceBook page, where one user, Aaron James Goodwin-O'Neill, said the reports seemed "a tad bit exaggerated.''
"I've used food grant cards to pick up the same kind of items for my ex girlfriend and even my mother in the past without a problem.''
People who read Ms Thompson's blog have also taken to Twitter to express their opinions about the issue using the hashtag UnnecessaryTampons.
@surlymermaid wrote: "Compulsory hysterectomies for all who are foolish enough to demand a benefit whilst being in possession of a uterus #UnnecessaryTampons."
@MoataTamaira wrote: "Ha! If you're banished to the menstruating hut at the borders of the village for the week you don't need #unnecessarytampons #knowyourplace."
But @caffeine-addict tweeted: "Hey peeps the #unnecessarytampons thing is a cock up. Of course WINZ provides this. If WINZ or supermarkets say otherwise they're wrong."
@chrisphilpottnz pointed out: "Do nappies count as 'luxury items'? Problem solved. #unnecessarytampons."
@CMRanapia tweeted: "Stupid whinging beneficiaries, you can make your own #unnecessarytampons out of lint, cat hair and garden twine."
And @juliefairey tweeted: "Look, we all know beneficiaries will just leap at the chance to get free tampons and on-sell them on the black market #unnecessarytampons."