The move will also extend to Big W and BWS stores, which are owned by the Woolworths Group, and is expected to be in place by July 2018.

Woolworths Group chief executive Brad Banducci said they currently give out more than 3.2 billion lightweight plastic bags a year.

"Our customers can expect further commitments in reducing plastic use in all parts of our supply chain, especially in fruit and vegetables,” he said.

Woolworths' latest move comes amid a growing social media campaign to 'ban the bag', which is calling on the premiers of NSW, Victoria and Western Australia to introduce state-wide bans of single-use non-biodegradable plastic bags.

The ACT, South Australia, Tasmania and Northern Territory have already banned plastic bags, and Queensland will implement a ban in mid-2018.

But Member for Cootamundra Katrina Hodgkinson said she saw no reason for the State Government to legislate a ban on plastic bags.

"I welcome Woolworths and Coles being responsible and taking charge on the phasing out of plastic bags in their stores," she said.

"What they have done is remove the need for the State Government to legislate because they have already taken the lead, this is a good thing because often legislating on an issue can bog it down in red tape.

"I believe in small government and Government putting the least impost on people as it can, so I congratulate the big players in the industry for taking charge and being environmentally responsible."

Ms Hodgkinson said there will always be some instances where plastic bags are still needed in a grocery store.

"Some circumstances need plastic bags such as when there are foods like raw meat that can contaminate other foods, " she said. "So consumers need be conscious of health issues, cross contamination, hygiene and food safety and still have plastic bags available for those instances where it will always be needed.

German supermarket chain Aldi, which opened in Australia in 2001, has never provided single-use plastic bags at the checkout and sells multi-use bags for 15 cents and fabric bags for 99 cents.