Chief executive David Potts said only those with medical exemptions will be allowed to shop without a mask from today (11 January).
He 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."
Matt Hancock said he 'applauds' the move at a Downing Street briefing.
Discussing whether rules might be tightened, he added: "We keep these things under review and we have demonstrated that we're willing to tighten the rules if they need to be tightened.
"But the thing that really matters right here, right now is that everybody follows the rules as they are today.
"And everybody can play their part in doing that. I want to see all parts of society playing their part in this."
It comes after Boris Johnson spoke to senior ministers about whether the current rules are having an impact - and he has warned that tougher measures may be needed.
It seems the government is honing in on one exemption in particular, which allows people to meet with one other person from outside their household. This is meant to be for exercise in a public space.
Speaking to the Daily Telegraph, a source said that the exemption is currently being used as 'an excuse for people to go for a coffee in the park with their friends,' adding: "It may be we tighten up on things like that."
It has also been reported that supermarket chains might be told to get tougher on customers social distancing and wearing face coverings.
Masks could also be introduced in busy outdoor areas like shop queues and even enclosed work spaces, such as offices.
Speaking to Sky News about stricter rules, vaccine minister Nadhim Zahawi said: "This virus loves social interaction, especially this new variant - so the worst thing you can do is socialise.
"We must make sure we only go out to exercise or necessary shopping - but stay at home."
He added: "We don't want to go any tougher but we need people to behave so we can bring the virus under control while we vaccinate and hit that target mid-February.
"These rules are not boundaries to be pushed against - they're to bring the virus under control and save lives. I know it's hard and we're all social animals."
Featured Image Credit: PA
Topics: UK News