Nigel Boyle, owner of Toy and Models Collector's Market, said his gut feeling was that the collectibles would be a "shortlived fad".
"Other things like miniature All Blacks and things like that have been popular in the past, and they quickly faded away.
"I'm sure they won't have any great value in years to come."
But Mr Boyle said the items were "cute" and would likely create nostalgia among collectors.
Marketing expert James Paterson, of Bay of Plenty Polytechnic, said the promotion was a marketer's dream due to the social media attention it was receiving.
"The publicity is always difficult to drum up, they are doing a wonderful job of it."
He believed its popularity was due to a combination of the use of iconic Kiwi brands and the "collectible" nature of it.
"They have got some quite iconic brands like Anchor, Sanitarium and Whittakers.
"That probably pulls people in, Kiwis feel in love with those sorts of brands.
"For people who start the collection, they want to carry on and get as many of them as they can."
New World spokeswoman Katherine Klouwens said demand had been greater than anticipated in the Western Bay, with all supermarkets having to re-order stocks of the accessories.
Customers had been driving from Mount Maunganui to Te Puke just to buy them.
"Some of the stores have received calls from customers as far away as Wellington trying to get their hands on more accessories.
"Customers have also been asking for the mini collectibles, some even inquiring if they could buy the entire set.
"Some of the stores have seen customers swapping at the check-out.
"It seems the iconic Kiwi brands are the most popular with customers."
The terms and conditions state that the items can't be sold, but it was difficult to police websites and stop online sales, Ms Klouwens said.
"We are, however, happy for customers to share and trade minis online."
Chelsea Werder, an admin on the "New World's Little Shop Collectibles Swap/Trade/ Sell Facebook page, said the addictive nature of the collection was unexpected.
"You have to spend $1760 [at New World] to get a set without double-ups, yet you can go to The Warehouse and get a full food set for maybe $20."