Sainsbury's will not "challenge" shoppers who enter its stores without a face covering, despite it becoming a legal requirement from Friday.
The supermarket giant said customers who enter its stores won't be questioned - as they may have a hidden disability.
It comes as the government prepares to make face coverings mandatory from July 24, in its latest fight against coronavirus.
The guidelines state that supermarket staff will not be required to wear face coverings, but Sainsbury's supermarket rivals have said customers will be required to don coverings from this weekend.
Under new rules, police will be able to fine those who refuse to wear a mask - while retailers will be able to refuse entry to those who refuse to don't comply.
In England, fines start at £100, though will be reduced to £50 if the person pays within 14-days. In Scotland, fines start at £60.
Sainsbury's, however, has told Twitter users: "We won’t be challenging customers without a mask when they enter or when they are in store since they may have a reason not to wear a mask."
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Elsewhere, rival supermarket Aldi said shoppers will be required to wear masks - however said customers should be mindful of those who may have a hidden disability.
In an email to shoppers, Aldi chief executive Giles Hurley said: "Last week, the Government announced that face coverings will be compulsory in shops in England from 24th July and, for that reason, you will need to wear a face covering to enter one of our stores from this date.
"Even as the country opens up again, I know many are concerned about safety and do not want the steps we are taking to move forward, to mean we take a step backwards in the fight against the virus.
"To those vulnerable customers, please rest assured that the measures we have introduced to give you safe access to affordable food, such as early opening times from Monday to Saturday, will continue and our home delivery grocery parcels are still available to purchase," he said.
"It has been heartwarming to see customers remembering that not all disabilities and health conditions are visible, and being considerate of others who may not be able to socially distance or wear a mask."
Under current rules, you don't have to wear a covering if you have "any physical or mental illness or impairment, or disability", and would experience "severe distress" from doing so.
This includes if you suffer from autism or are a child under the age of 11.
See our guide on face mask exemptions and how to apply for a card, here
