Supermarkets have warned the rising number of retail workers being forced to self-isolate is beginning to affect the availability of some products.
The Co-op said it was "running low on some products", while Iceland said shops might have to be shut.
Sainsbury's said it "might not always" have the exact products people wanted, but downplayed fears of shortages saying the problem was not widespread.
Iceland also urged shoppers not to panic buy, saying it was not necessary.
Business Secretary Kwasi Kwarteng said the government was "concerned about instances of shortages".
"I don't want people to get the impression that every shelf in every supermarket is bare - that is not the case but we are certainly concerned about instances of shortages, we are looking at the supply chains of critical industries and we are reviewing that situation," he added.
A record 618,903 people in England and Wales were "pinged" by the NHS Covid app in the week to 14 July.
Supermarkets and other sectors, including hospitality and transport, have said growing numbers of staff have been affected which means they have to self-isolate for 10 days. Some companies have reduced opening hours to cope with the staff shortages or shut parts of the business.
Firms want people who have been doubly vaccinated or have daily tests to be able to return to work.
'Isolated incidents'
Mr Kwarteng said that the government would publish guidance later on which sectors would be exempt, although he declined to comment on whether it would include the food industry.
Many of Thursday's newspapers carried pictures of empty shelves in some supermarket branches - with some describing panic buying of certain items - but industry sources told the BBC that so far, food shortages were not a systemic problem.
Iceland's managing director, Richard Walker, said photographs of empty shelves in supermarkets were "isolated incidents".
It is understood that Tesco is experiencing low availability across a small number of products due to the rise in the number of workers self-isolating as well as the industry-wide shortage of HGV drivers.
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