Lord Rose said there was no shortage of food in the country and stressed that “nobody will starve”.
“There is a billion pounds more food in people’s larders than there was a couple of weeks ago — what are they doing with it? How much food do you need to eat? How much do you need to store away?
“Please show some restraint,” he told BBC Radio 4’s Today programme.
“There is no shortage of food … Nobody will starve.”
Lord Rose, a former boss of Marks & Spencer, contracted the virus and self-isolated. He said he ventured out to the supermarket for the first time in two weeks on Wednesday.
The online supermarket boss said Britons should avoid going to supermarkets at peak hours and only buy what they need.
He called on Britons to “make your meals work”.
“If you buy a chicken, roast the chicken, have the roast chicken dinner, the following day turn it into a stir fry, the following day make it into soup,” he said.
“You can make a relatively small amount of food go a long way and I think we live in a very profligate society today — we buy too much, we eat too much and we have to learn new ways.”
Ocado has been operating at capacity during the crisis, and on Tuesday said it had around 10 times more demand for its services than it did before the outbreak began.
Some British supermarkets have introduced stricter measures to protect their customers and staff.
Tesco boss Dave Lewis has written to customers saying staff will draw new floor markings in the checkout areas, install protective screens on checkouts, and introduce one-way aisles.
“Our social distancing plans aim to protect customers from the moment they enter our car parks, to browsing products, to paying and finally exiting our stores,” he wrote.
In a letter to customers, Sainsbury’s chief executive Mike Coupe said the number of people allowed in stores and at ATMs at any one time will be limited.
He said queueing systems will be put in place outside stores and people are urged to arrive throughout the day to avoid long queues forming in the morning, and encouraged people to pay by card.
“We will be reminding people in stores to keep a safe distance from other customers and from our colleagues,” he said.
Mr Coupe said the number of checkouts will be reduced and screens will be introduced.
He said many customers have written to him to say they are elderly or vulnerable and are struggling to book online delivery slots.
“We are doing our absolute best to offer online delivery slots to elderly, disabled and vulnerable customers. These customers have priority over all slots.
“Our customer careline has been inundated with requests from elderly and vulnerable customers — we have had one year’s worth of contacts in two weeks.
“We have proactively contacted 270,000 customers who had already given us information that meant we could identify them as being in these groups,” he said.
Mr Coupe, who apologised to regular online customers, said they have already booked in slots for 115,000 elderly, disabled and vulnerable customers this week.
Meanwhile, Sainsbury’s said it is temporarily closing 12 convenience stores that have seen “significantly fewer customers in recent days as people are working from home”.
The employees will move to neighbouring stores until these stores re-open.
Elsewhere, shoppers at Asda have seen changes including markers on the floor to help them keep two metres apart, barriers, signs and announcements. The supermarket has also asked shoppers to ditch cash in favour of card payments.
Lidl has announced it will install new donation boxes in store to collect for vulnerable families, extending a scheme that has been in place since 2017.
All non-essential stores have been forced to close as Britons are told to stay inside as much as possible, and only leave for supplies and a brief daily exercise.
Additional reporting by agencies