The supermarket chain is also asking customers to shop alone, rather than in larger groups.
Trained security guards will challenge anyone who doesn’t follow the rules, Sainsbury’s said.
The company’s announcement comes after Morrisons said customers who are not medically exempt and refuse to wear a mask will be asked to leave stores.
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Simon Roberts, managing director of Sainsbury’s, said the company had written to customers to inform them of the changes, which he said followed testing last weekend.
He said: “I have spent a lot of time in our stores reviewing the latest situation over the past few days and on behalf of all of my colleagues I ask our customers to help us keep everyone safe.
“The vast majority of customers shop safely, but I’ve also seen customers try to shop without a mask and shop in larger family groups.
“Help us keep all of our colleagues and customers safe by always wearing a mask and shopping alone.
“The care and consideration of everyone is more important than ever. ”
The supermarket giant said it has significantly reduced the number of customers allowed into stores at the same time and is deploying staff at the entrances to stores to help with cleaning and social distancing.