Shoppers who refuse to wear a face covering will be barred from Morrisons.
From Monday, those who decline to wear a mask without a medical exemption will not be allowed inside the supermarket chain’s shops.
Sainsbury’s also said it would challenge customers not wearing a mask as well as those shopping in groups.
The move comes amid concerns that social distancing measures are not being adhered to in stores across the UK.
Morrisons chief executive David Potts said: “Those who are offered a face covering and decline to wear one won’t be allowed to shop at Morrisons unless they are medically exempt.
“Our store colleagues are working hard to feed you and your family, please be kind.”
Tesco and Sainsbury’s said safety remained their “highest priority”, and that customers were given regular reminders to follow the rules.
Sainsbury’s later confirmed it will post trained security guards at shop entrances to “challenge” any customers not wearing a mask or shopping in groups.
Chief executive Simon Roberts said: “I’ve spent a lot of time in our stores reviewing the latest situation over the last few days and on behalf of all my colleagues I am asking our customers to help us keep everyone safe.
“The vast majority of customers are shopping safely, but I have also seen some customers trying to shop without a mask and shopping in larger family groups.
“Please help us to keep all our colleagues and customers safe by always wearing a mask and by shopping alone. Everyone’s care and consideration matters now more than ever.”
A spokeswoman for Sainsbury’s added guidance remained “shop alone if you can” and customers with children or carers would not be refused entry.
Tesco said it was still enforcing social distancing practices in store but was not looking yet at reintroducing measures such as one-way aisles.
Shopworkers’ union Usdaw said that it had been “inundated” with complaints from its members – who are classed as key workers – and called for supermarkets to revert to more stringent in-store measures.
Prime Minister Boris Johnson said people needed to “do the right thing” by adhering to social distancing when out.
Retail bosses have also suggested that further police support is needed to help enforce measures, which they say are leading to an increase in abuse towards staff.
Usdaw general secretary Paddy Lillis said: “Retail staff are working with the public every day and not only suffer increased abuse, but are deeply worried about catching Covid-19.
“Where safety measures are agreed, retailers need to make sure that they are being followed consistently, in every store.
“We are also very concerned by reports that too many customers are not following necessary safety measures like social distancing, wearing a face covering and only shopping for essential items.
“Many retail workers are at a greater risk of catching the virus and bringing it home to their families.
“These key workers must be valued, respected and protected.”