One retailer said they can be "unhygienic" at the best of times, and people should take care to wash them if they are reusing bags.
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British food delivery service Ocado announced last month they would be rejecting old shopping bags because of coronavirus.
They said last month: "Following the latest advice from the World Health Organisation, we have temporarily paused our bag recycling scheme."
"Please do not hand any used bags back to your driver: they will not be able to take them."
But other supermarkets have continued to allow customers to reuse their bags.
Entire states in the US have now banned the use of reusable bags.
One US supermarket Green Zebra said they had to reverse their policy on reusable bags.
Green Zebra founder and CEO Lisa Sedlar told HuffPost: "In the best of times, reusable bags can be unhygienic because a lot of people don't wash them with soap and water after each use."
"During this unprecedented time, it's a life-and-death important to protect everyone's health, so it wasn't a hard decision to ban the use use of reusable bags."
According to a study from the National Institute of Health the virus can live on stainless steel surfaces for as long as three days.
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One of the scientists from the study, Vincent Munster said it could linger on lots of different kinds of surfaces.
He said: "We speculate due to the porous material, it desiccates rapidly and might be stuck to fibres."
A study from the International Association for Food protection showed that over 50 per cent of reusable bags contain large quantities of bacteria – and may even contain E. Coli and faecal matter.
At American supermarket giant Trader Joe's stores, customers are still allowed to bring bags from home, provided they package their own groceries.
Starbucks has banned the use of reusable coffee cups across its UK stores over fears of spreading COVID-19.
The coffee chain's Europe spokesman Robert Lynch said: "Out of an abundance of caution, we are pausing the use of personal cups or tumblers in our stores across the UK.
"However, we will continue to honour our 25p discount for anyone who brings in a personal cup."
Starbucks suspended its 5p charge for customers asking for paper cups.
Food safety expert Jeff Nelken said people can still safely use bags if they clean them after every use.
Mr Nelken said disinfectant wipes can do the trick of getting rid of any nasty bacteria.
A homemade disinfecting solution with four teaspoons of unscented bleach for every four cups of water can also do the trick.
It can be easily mixed into a spray bottle to spray onto bags, and wiped down with a towel.
The home-made mix works just as well for plastic bags as it does fabric – but do a spot tests on fabric bags to make sure there's not discolouration.