Speaking during the daily Downing Street briefing on Saturday afternoon, Environment Secretary George Eustice urged people not to panic-buy.
He said: "We recognise that this is a challenging time and there are many things the Government is asking the nation to do differently as we work together to fight this pandemic.
"Be responsible when you shop and think of others.
"Buying more than you need means others may be left without.
"We all have a role to play in ensuring we all come through this together."
Asked about possible Government intervention restricting food purchases, Mr Eustice said: "The reality is that most of the supermarkets are already, of their own accord, putting limits on certain items so I don't think it is necessary or appropriate for the Government to dictate this."
He said people need to "calm down" and "only buy what they need".
Stephen Powis, national medical director at NHS England, said people should be "ashamed" of themselves for panic-buying, and urged people to think of struggling NHS staff.
"I would like to make a plea on behalf of all my colleagues in the NHS, nurses, doctors, paramedics and many, many others who are working incredibly hard at the moment to manage this outbreak of coronavirus," he said.
"It's incredibly important that they too have access to food, to those essential supplies that they need."
Mr Powis made reference to a video posted on social media of a critical care nurse named Dawn, who was reduced to tears after being unable to find any fruit or vegetables in the supermarket.
"Frankly we should all be ashamed that that has to happen - it's unacceptable.
"These are the very people that we all need to look after perhaps us or our loved ones in the weeks to come."
Helen Dickinson, chief executive of the British Retail Consortium, said she wanted to reassure people that those "right across the food industry... are doing everything they can to ensure that we have the food we all need."
Ms Dickinson said: "There is plenty of food in the supply chain.
"The issue is around people and lorries, so getting that food right into the front line onto our shelves, which is why we've seen some shortages."
Ms Dickinson added: "There is a billion pounds more food in people's houses than there was three weeks ago, so we should make sure we eat some of it."