Greene King has been forced to close 33 pubs in the past week due to staff shortages caused by people being forced to self-isolate by the NHS Covid app.
Greene King boss Nick Mackenzie said the pubs group had also had to shorten opening hours in some circumstances.
“I think this is a problem,” he told the BBC. “It could get worse.”
Recent figures showed more than 500,000 people in England and Wales were “pinged” by the app in the week to 7 July, up 46% on the previous week.
People who have come into contact with someone who has tested positive for Covid-19 must self-isolate for 10 days.
At the weekend, Marks & Spencer said it may have to reduce store opening hours if the rate of workers self-isolating continues to rise. While a leading supermarket, which declined to be named, told the BBC “there’s a risk that there won’t be sufficient staff to open shops”.
Mr Mackenzie said: “Across the industry, we think the number is about one in five of our team members who have been affected by this and therefore it is causing a real issue for us setting-up a business on a daily basis.”
PureGym’s chief executive, Humphrey Cobbold, said his business had managed to keep all of its sites open despite rising numbers of employees forced to self-isolate, “but it’s been a very close call”.
He said: “Up to 25%, in some areas, of our staff have been asked to self-isolate.
“Through flexibility and sharing of labour across sites, we’ve been able to keep sites open so far but it’s been a very close call in certain circumstances.”
Staff shortages have grown as England lifted final Covid restrictions on Monday, including the legal requirement to wear a face covering to prevent the spread of the virus.
Wales is expected to scrap most rules on 7 August though this will not include face masks. Scotland has moved to the lowest level of restrictions of Covid restrictions but face coverings must be worn for a further three weeks. Northern Ireland will decide on Thursday to ease rules on seven days’ time.
The Confederation of British Industry has warned that “crippling staff shortages” risks hampering an economic recovery.
It has called for an immediate end to the 10-day self-isolation period for people who have been fully vaccinated. It also said daily lateral flow tests could help people who have not received both jabs get back to work.
From 16 August, people who have been fully vaccinated will not have to self-isolate if they are “pinged” by the NHS app when they have come into contact with someone who has tested positive for Covid. They will instead be advised to take PCR test as soon as possible.
Mr Mackenzie said the government needs to bring the “test and release” scheme forward to allow more people to come into work and “get us back to normal again”.
“That’s all we’re really asking for, let’s get back to some normality,” he said.