The supermarket giant has put restrictions on essential items in some stores.
Tesco CEO Dave Lewis said panic buying is “unnecessary” and that it “creates a tension in the supply chain”.
Some Tesco stores have also put restrictions on groceries including flour, pasta and toilet roll.
A Tesco spokesperson said: “To ensure that everyone can keep buying what they need, we had introduced bulk-buy limits on a small number of products.”
Asda stores have been reviewing the situation and are prepared to act if necessary.
The retailer has urged customers to only buy what they need so that they do not need to introduce restrictions.
A statement said: “To ensure there is enough for everyone, we will occasionally place purchase limits on certain products that are in high demand.
“Please shop responsibly so there’s enough to go round.”
Last month, Morrisons was among the first to put buying restrictions on popular items.
Purchases were restricted to three per item on products including toilet roll and disinfectant.
This was done to make sure there is enough stock for everyone to get what they need.
A Morrisons spokesperson said: “We are introducing a limit on a small number of key products, such as toilet roll and disinfectant.
“Our stock levels of these products are good but we want to ensure that they are available for everyone.”
Those visiting the discount retailer could notice restrictions on some items.
The retailer has asked customers not to buy more than they need.
While there are no set restrictions, each store is able to apply their own buying restrictions if necessary.
A spokesperson stated: “We want to reassure our customers that we are not currently experiencing any product shortages and have good availability in our stores.
“We hope all customers remain mindful of others when shopping with us to ensure everyone continues to have access to the products they need.
“Nonetheless, it is at our store managers discretion, should customers start to bulk-buy, to limit the purchasing of specific items at that store.”