Morrisons will bar customers who refuse to wear face coverings from its shops amid rising coronavirus infections.
From Monday, shoppers who refuse to wear face masks offered by staff will not be allowed inside, unless they are medically exempt.
The announcement comes amid concerns that social distancing measures are not being adhered to in supermarkets.
Vaccines minister Nadhim Zahawi said the government is "concerned" shops are not enforcing rules strictly enough.
"Ultimately, the most important thing to do now is to make sure that actually enforcement - and of course the compliance with the rules - when people are going into supermarkets are being adhered to," Mr Zahawi told Sky News.
"We need to make sure people actually wear masks and follow the one-way system," he said.
Morrisons said it had "introduced and consistently maintained thorough and robust safety measures in all our stores" since the start of the pandemic.
But it said: "From today we are further strengthening our policy on masks."
Security guards at the UK's fourth-biggest supermarket chain will be enforcing the new rules.
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."
Earlier on Monday, Mr Zahawi stopped short of saying that supermarket staff should be responsible for enforcing rules on face masks.
Enforcement of face coverings is the responsibility of the police not retailers. Wearing face masks in supermarkets and shops is compulsory across the UK.
In England, the police can issue a £200 fine to someone breaking the face covering rules. In Scotland, Northern Ireland and Wales, a £60 fine can be imposed. Repeat offenders face bigger fines.