Chief Executive David Potts said those who break the rules will be denied entry unless they are medically exempt.
In a plea urging clients to “be nice,” he said members of the public and frontline staff should not be put at risk.
“Those who are offered a face mask and refuse to wear one will not be allowed to shop at Morrisons unless they are medically exempt,” Potts said.
“Our colleagues in the store work hard to feed you and your family, please be kind. ”
It comes after the Usdaw union revealed it has been “inundated” with complaints from members who say they are “deeply concerned” for their safety as members of the public flout Covid measures in stores.
Usdaw urged supermarkets and food retailers to revert to “tight” restrictions and said staff – who are classified as key workers – must be “valued, respected and protected”.
Chains such as Tesco and Sainsbury’s have said safety remains their “top priority” and customers are regularly reminded to follow the rules.
It comes as Vaccines Minister Nadhim Zahawi has expressed concerns that members of the public are not complying with measures put in place by supermarkets, when restrictions may need to be tightened.
“I’m worried that supermarkets and people wear masks and follow the one-way system and make sure that when they’re at full capacity they are waiting outside the supermarket,” he said. .
Usdaw General Secretary Paddy Lillis said: “Retail staff work with the public every day and not only suffer from an increase in abuse, but are deeply concerned about catching the Covid-19.
“When security measures are agreed upon, retailers need to ensure that they are consistently followed in every store.
“We are also very concerned about reports that too many customers are not following necessary safety measures such as social distancing, wearing a face mask and only purchasing essential items.
“The vaccine rollout is going to take some time and we can’t afford to be complacent in the meantime, especially with a new strain sweeping the country.
“Many retail workers are at greater risk of catching the virus and bringing it home to their families.
“Supermarket workers and delivery drivers have worked throughout the pandemic to maintain the country’s supply of essential commodities.
“These key workers need to be appreciated, respected and protected. ”
A Sainsbury’s spokesperson said: “Safety remains our top priority.
“We continue to implement a range of measures to ensure the safety of customers and colleagues in our stores.
“We have hosts outside our busy supermarkets and convenience stores to limit the number of customers entering stores and continue to remind customers to wear headwear and shop on their own if they do. can.
“We also have posters and regular announcements from Tannoy. ”
Tesco said it still maintains in-store social distancing practices, but is not yet seeking to reintroduce measures such as one-way aisles.
“The safety of our customers and colleagues is our top priority and we have already implemented extensive social distancing measures in our stores to ensure that everyone can shop safely with us,” the store said on Twitter.
“We ask all of our customers to wear a face mask when visiting our stores and to put up prominent signs informing customers of the rules.
“However, some clients may not be able to wear face coverings for medical or safety reasons and we have asked our colleagues to respect this and not directly challenge them. ”
Data from Public Health England last week revealed that 11 outbreaks of the disease originated from grocery stores.
But England’s chief medical officer Professor Chris Whitty said supermarket staff would not initially be prioritized for vaccinations unless they also fall into the highest vulnerability categories.
Get the latest money tips, news and help delivered straight to your inbox – sign up at mirror.co.uk/email
Responding to a question from a Somerset food retail worker on BBC Radio 5 Live, he said: ‘All of us in the company have relied on the extraordinary work of people who have kept essentials retailing. – food, etc. I think we should all thank you and your colleagues for that.
“In terms of prioritization of vaccination… the first wave concerns people who have the greatest risk of dying, it’s a clinical question, largely about age.
“Obviously if someone falls into that, if they’re a senior working in the retail business or have a health issue, they’ll be included in that. ”
Professor Whitty added that as soon as the most vulnerable were vaccinated, ministers would decide who to prioritize.