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But they say supermarkets have learned from past outbreaks and are prepared for Omicron, a highly transmissible strain. Provided people don't stockpile, there should be ample supply for everyone.
One Auckland shopper said they didn't receive any nappies in their click and collect order on Thursday and decided to visit New World Birkenhead.
"I popped in store and they legit had like 2-3 packs of nappies, all in newborn size," the shopper said.
"I then went to put my click and collect order in for next week and add nappies to my cart and they were showing as not having anything available in most sizes too."
The shopper also noticed it was low on baby wipes.
"This morning my husband went to the Warehouse at Glenfield mall and said it looked like people were stockpiling as there were hardly any there and someone was restocking the shelves as he left."
Yesterday, Prime Minister Jacinda Ardern confirmed that there won't be lockdowns when Omicron spreads widely but New Zealand will move to the red traffic light setting within 24-48 hours of it entering the community.
Countdown's director of corporate affairs, safety and sustainability Kiri Hannifin said stores are in "pretty good shape at the moment" and there are no limits in place.
"Provided people are not stockpiling and only picking up a couple of extras in their shop, there will continue to be plenty available for everyone," she said.
However, corporate affairs manager at Foodstuffs Emma Wooster said customers at their New World, Pak'nSave and Four Square stores may start to see limits on certain products.
"Customers may start to see limits to the number of certain products in any one shop, this is to ensure there is a consistent flow of product onto the shelves and fair opportunity of product for all of our customers."
Wooster said as the pandemic evolves, supermarket staff are revising their operating procedures in response to Covid-19.
"While it's not possible to exactly predict how Omicron will behave if it takes a hold in New Zealand, we've had the benefit of seeing and learning how the variant has impacted supply chains overseas, as well as this we are able to manage our supply chain end-to-end.
"This puts us in a strong position to prepare for, and protect ourselves, from this particularly transmissible variant of the virus," she said.
Due to the ongoing pandemic, Wooster said the global supply has been affected and expects it to continue into this year.
While Omicron may throw up some more challenges, Hannifin said Countdown is working with suppliers to prepare.
"We're working closely with our suppliers and supply chain partners and doing everything we can to be prepared right across our supply chain - from our growers and food manufacturers through to our transport and logistics partners, distribution centres and store network - to ensure we can keep stock flowing onto shelves."
In terms of shoppers, Hannifin asked customers to wear masks in store, practise physical distancing and treat staff and other customers with "kindness and respect."