Effective July 1, they also are being asked to carry their own reusable bags for fruits and vegetables.
The latest move is part of a wider government campaign against single-use plastics.
In July 2019, New Zealand no longer allowed stores to provide single-use shopping bags with handles that are made of plastic up to 70 microns in thickness.
The new ban will eliminate 150 million plastic produce bags from circulation each year or 17,000 plastic bags every hour.
In October, it proposed taxing the greenhouse gases produced by farm animals like sheep and cattle.
The world's first scheme will see farmers paying for agricultural emissions in some form by 2025.
The country's farming industry accounts for about half of its emissions.