The coverings will be a legal requirement for anyone shopping on the high street or in supermarkets, with a risk of a £100 fine for anyone not following the rules.
But a number of supermarkets have said they will not challenge shoppers who don't wear them.
In a Tweet to followers, Sainsbury's said they won't challenge customers as they could have a hidden disability.
The question was asked by a follower who asked if staff would be enforcing the rules.
In reply, Sainsbury's said: "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."
Lidl have also said they won't be challenging their customers.
They Tweeted: "In line with government guidance, wearing a face covering in store is the responsibility of the individual, not the retailer, and should only be enforced by Police."
Tesco also said on Twitter that they wouldn't be refusing any of their customers entry.
They stated: "We understand some people cannot wear face coverings and colleagues should not challenge customers who are not wearing a face covering and must not stop customers from entering the store or from being served."
Aldi said shoppers will be asked to put on their masks, but added that customers shouldn’t judge others if they are not wearing one.
Government guidelines state that people don't have to wear a face covering if they have 'any physical or mental illness or impairment, or diability,' and would experience 'severe distress' from doing so.
Children under 11 are also exempt from covering their faces, as well as those with autism.