The supermarket chain Countdown has pulled plastic straws off its shelves.
The ban that takes effect from today is expected to result in 11.6 million fewer plastic straws being thrown away each year.
The company's spokesperson, Kiri Hannifin, said the plastic straws were an environmental problem and that removing them from sale was the best option.
"We've looked far and wide for alternatives and we've got on offer bamboo straws, paper straws, metal straws and we are also looking at straws made of silicone," she said.
The supermarket chain is also phasing out the use of plastic bags at the checkout.
The move follows an announcement in July by Starbucks that the it would eliminate plastic straws from its stores world-wide by 2020.
The US coffee retailer will phase out single-use straws from its more than 28,000 locations, cutting out an estimated one billion straws each year.
Customers will instead be given plastic lids designed for use without a straw or with non-plastic straws.