The discount department store chains, which are both owned by Wesfarmers, which also owns Coles, will instead keep single-use bags in stores until an unknown date in 2019.
Coles will get rid of plastic bags on Sunday.
It incorporated a specialist being ambushed by a client in the wake of being told there were no free plastic bags at a store in Western Australia state.
More than 8 million tonnes of plastic ends up in the world's oceans each year, according to United Nations, which has called for single-use bags to be eliminated completely by 2022.
Australian supermarket workers have found themselves at the front line of an angry consumer backlash over moves to ban single-use plastic bags, with a vocal minority abusing cashiers and one customer wrapping his hands around an employee's throat, union officials said Monday. Are you concerned about the single-use bags being banned?
Retail giants Woolworths and Coles announced last month new goals to reduce plastic products and packaging in response to customers wanting a greener shopping experience.
A ban on the use of disposable plastic bags is part of the national policy on waste reduction.
Mr Paramor said the difference in legislation around the country meant retailers had more wriggle room in some states than others.
Chains such as Myer and David Jones and fashion retailers generally use thicker bags made of low density polyurethane.
Target's lethargy on plastic bags is surprising as they were once a leader in the retail sector on the sustainability of shopping bags.
'Ethnic Cleansing': Israel Begins Demolition of Palestinian Bedouin Village Khan al-Ahmar
Israeli authorities demolished a school in the community in February, saying it had been illegally built. Sources added that Israeli police deployed near the Bedouin village blocked the main road.
Shoppers down under are apparently fighting with supermarket staff because they're unhappy at having to pay 15 cent (8p) for the bags.
Australians aren't taking the plastic bag charge as well as we did.
Australia's biggest supermarket chains are scrambling to combat "bag rage" as frustrated shoppers vent their anger over the removal of single-use plastic bags.
Woolworths will be giving away reusable bag for 10 days.
'It'll take a little while for some members of our public to get used to remembering to take their reusable bags, but it won't take long until many of us just use it as everyday practice, ' she said.
"While some customers have forgotten their reusable bags altogether, many have done the right thing and brought their own only to end up one or two reusable bags short".
Queensland retailers face a fine of up to A$6307.50 (NZ$6886) for giving a plastic shopping bag to a customer to carry goods from their premises, whether or not they charge for it.
To prevent any dramas, every Coles checkout will be open with additional staff to assist customers and make the transition as flawless as possible.
The hope is it will speed customers through the store even if they do struggle with adapting to shopping without traditional bags.