Several Iceland stores have been forced to close after staff were told to isolate by the NHS Covid app.
People who have come into contact with someone who has tested positive for the virus must self-isolate for 10 days.
The latest figures showed more than 500,000 people in England and Wales were notified by the NHS app to self-isolate in the week up to July 1.
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Richard Walker, managing director of the supermarket group Iceland, said around four per cent of the total workforce were currently absent because of coronavirus.
Due to the staff shortages, Mr Walker said several stores have had to close.
He told the BBC: "We have got over 1,000 people absent due to Covid, that's the highest ever since testing began.
"It's about 4% of our total workforce of 30,000.
"In fact, we have just announced employing an additional 2,000 people on top of that to give us a deeper pool of labour, because so many people are now getting pinged."
Asked about the impact on the business, he said: "A number of stores have had to close and the concern is that as this thing rises exponentially, as we have just been hearing, it could get a lot worse, a lot quicker."
Marks & Spencer chief executive Steve Rowe said the company may have to change their opening hours due to staff shortages.
He told The Times: "Our Covid cases are roughly doubling every week and the pinging level is about three to one of Covid cases, so we’re seeing that growing exponentially.
“If there’s [staff] shortages we’ll have to manage it by changing hours of stores, reducing hours."
