The supermarkets made the announcements in a bid to help combat rising coronavirus infection rates.
As of Monday, January 11, Morrisons shoppers without masks won’t be permitted entry unless they are medically exempt.
Sainsbury’s also said it would challenge those not wearing masks or shopping in groups.
The supermarket’s 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."
Trained security guards will also be placed at supermarket entrances.
David Potts, chief executive of Morrisons, earlier 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."
He added: "Our store colleagues are working hard to feed you and your family, please be kind."
Earlier today, vaccines minister Nadhim Zahawi said the Government was "concerned" shops are not enforcing rules strictly enough.
He told Sky News: “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.
"We need to make sure people actually wear masks and follow the one-way system.”
Meanwhile, a worrying new study suggests that brain damage usually associated with strokes can be caused by your body battling off coronavirus.
Scientists used an MRI scanner to study brain tissue samples from patients who died after becoming infected.
They saw signs of damage caused by "thinning and leaky" brain blood vessels.
Researchers say it may have been caused by the "body’s inflammatory response to the virus".
But the team from the National Institutes of Health (NIH) in the US saw no signs of Covid-19 in the samples.
They say this suggests the damage was not caused by the virus directly infecting the brain.
Avindra Nath, clinical director at the NIH’s National Institute of Neurological Disorders and Stroke, said: "We found that the brains of patients who contract infection from SARS-CoV-2 may be susceptible to microvascular blood vessel damage.
"Our results suggest that this may be caused by the body’s inflammatory response to the virus.”