The supermarket giant has announced plans to reserve the first hour of shopping at all its stores for elderly and vulnerable customers.
The special shopping hour will take place tomorrow, Thursday, March 19.
Chief executive Mark Coupe said: "I have listened to feedback from you and from Sainsbury’s colleagues across the country and wanted to share some of the extra steps we are taking to make sure everyone has access to the items that they need.
"A number of you suggested that we reserve an hour in stores for elderly and vulnerable customers. In response to this request, we will set aside the first hour in every supermarket this Thursday, 19th March, for elderly and vulnerable customers.
"If you or an elderly family member, friend or neighbour would like to shop during this hour, please check online for your local supermarket opening hours. For all other customers, supermarkets will open one hour after the published opening time.
"I hope that you can respect this decision and will work with us as we try our best to help those that need it the most."
Mr Coupe urged customers to avoid panic shopping, saying that there was enough food for everyone "if we all just buy what we need".
Sainsbury's has introduced limitations on certain products, and has warned that customers will now be able to buy a maximum of three of any grocery product and a maximum of two of the most popular, including toilet paper.
Mr Coupe said: "We have enough food coming into the system, but are limiting sales so that it stays on shelves for longer and can be bought by a larger numbers of customers."
The company will also close their meat, fish and pizza counters from Thursday to allow staff to focus on keeping shelves stocked.
It is understood that the offer applies only to the company's superstores, which will have received deliveries before opening.
This means that the Sainsbury's store on Falsgrave in Scarborough will be open only to elderly and vulnerable people tomorrow morning from 7am and everyone else from 8am until it closes at 10pm.