The food retailer is running a trial in eight stores from Monday which will see sturdy paper bags offered at checkouts instead.
If the trial is popular, introducing paper bags only across all its 494 stores would save 90 million plastic bags being used annually, the equivalent of 3,510 tonnes of plastic per year, the company said.
Chief executive David Potts said: “We believe customers are ready to stop using plastic carrier bags as they want to reduce the amount of plastic they have in their lives and keep it out of the environment.
“We know that many are taking reusable bags back to store and, if they forget these, we have paper bags that are tough, convenient and a re-useable alternative.”
The proposed paper bag can carry up to 16kg, has handles, can carry a similar amount of items as its plastic counterpart and is easily recyclable, the food retailer added.
Last year Sainsbury’s said it was the first UK supermarket to remove plastic bags for loose fruit, vegetables and bakery items.
Tesco has said it will stop using plastic bags to deliver online groceries following a successful trial last year, saving nearly 2,000 tonnes of plastic annually.
Recent figures show the number of single-use plastic bags distributed by the big supermarkets in England has fallen more than 95% since the 5p charge was introduced in 2015.
Data from the Environment Department (Defra) shows the main retailers sold 226 million single-use bags in the past financial year, 322 million fewer than in 2018/19.
An estimated 7.6 billion bags a year were handed out by the leading supermarkets before the 5p charge was introduced in 2015.