Pensions administrator David Robb (59) raised his concerns after a trip to the Hardengreen store, Dalkeith, where he witnessed customers flouting the guidelines and yet not being challenged.
Mr Robb received a response from the supermarket telling him the company had made a decision to not challenge people entering their stores.
Tesco told the Advertiser the safety of its colleagues and customers was its “top priority”.
Recalling his trip to the store last month, Mr Robb said: “Four teenage girls entered the store laughing and giggling as they walked through the store with no face coverings. Nor were they challenged by any staff member.
“Two managers didn’t bat an eyelid as they passed by.
“As I went around the store I saw some other people without masks. A young couple in their 20s, another couple with a kid, all without masks.
“This is most concerning, especially following the outbreak in Hawick being linked to another supermarket.
“Tesco are basically saying they will not challenge anybody, so what’s the point in the government making it mandatory to wear them in shops?”
After initially being impressed with Tesco’s efforts during the Covid-19 pandemic, Mr Robb is concerned its policy on facemasks could lead to more outbreaks.
He said: “During lockdown I thought Tesco did well with people queuing to go in, and cleaning trolleys. But they have let it all go now.
“If the supermarkets are just letting people in willy-nilly it’s breaking the law. There have been cases centred around supermarkets, in Glasgow as well as Hawick.
“It would just take someone on the door as a ‘meeter and greeter’. That’s all they need. If people have a medical condition that means they can’t wear a mask then that’s fair enough. But looking at the people I saw in the store I wouldn’t have thought they had medical problems.
“It just didn’t make sense. There were no checks. They are basically flouting the law, but not giving reasons why.
“Why do they think they are above the law?”
A Tesco spokesperson said: “The safety of our colleagues and customers is our top priority and we are encouraging all customers to follow our social distancing measures, including wearing face coverings when shopping with us.”
All customer-facing Tesco staff have to wear face coverings, unless they cannot do so for medical or safety reasons, or if they are already working behind a protective screen.
A Scottish Government spokesperson said: “For those who are not exempt, it is mandatory to wear a face covering on public transport and in shops and other retail outlets to minimise the spread of the coronavirus.
“Retailers can ask people to wear a face covering - but we do not expect staff to enforce the wearing of face coverings.
“The police can issue fines if necessary.”