South Australia, ACT, the Northern Territory and Tasmania have already implemented state-wide bans, and Queensland plans to do so next year.
Woolworths yesterday announced its decision to phase out the bags, by June 30 next year.
Instead it would offer more durable, re-usable plastic bags at a cost of 15 cents, as well as multi-use hessian bags.
Studies have shown however that some types of reusable bag are not environmentally friendly in comparison unless they have been used 50, or even 100 times.
All stores across the Woolworths Group - including Woolworths Supermarkets and Metro stores, BIG W, BWS and Woolworths Online - would be covered by the changes.
Woolworths alone currently gives out 3.2 billion lightweight plastic bags per year in Australia.
Coles made a similar announcement just three hours after, saying the company had been working towards it for some time.
Coles is the parent company of Countdown in New Zealand, where the total number of single-use plastic bags each year is about 1.6 billion.
New Zealand councils and mayors have previously called for a national levy on single-use plastic bags, saying they impose significant environmental and cleanup costs.
The government has backed a soft plastic recycling scheme, but currently less than 2 percent of New Zealand's plastic bags are recycled.
School children also staged a protest outside Parliament last month, urging a ban.