The Government is insisting there is no need for people to panic buy.
It is not ruling out implementing a limit on how much people can buy - but says the food supply is robust and there is enough food and medicine available.
Business Minister Heather Humphreys says there is plenty of stock.
She has met with retailers and distributors who told her there is sufficient supply in the system.
"I met with the retailers, I met with the distributors and they have assured me that there is sufficient in the supply chain.
"If people go out and buy products that they don't need - to stockpile them - they're going to cause a problem.
"So I would say there is no need to do that, there is quite sufficient in the supply chain".
Ibec group Retail Ireland has moved to reassure people that retail supply chains are functioning as normal.
However it warns that distribution networks are "not designed" to cope with widespread bulk buying.
Retail Ireland Director Arnold Dillon says: "While there has been significant elevated demand for certain non-perishable grocery products, supply chains are functioning as normal and were well-placed to respond.
"However, retail distribution networks are not designed to deal with bulk buying on a widespread basis.
"It is important that consumers behave responsibility and don't buy more than they need.
"Retailers are working with their suppliers and monitoring consumer behaviour to avoid any shortages."
And Retail Excellence says: "The industry has never been more prepared having planned for a hard Brexit over the past number of months.
"Minister Heather Humphreys... has done a tremendous job in monitoring this matter and please be assured that we have more than adequate contingencies in place.
"Social media images of empty shelves are simply sensationalizing the matter. These shelves are restocked every evening and restocking will continue into the future."
"We echo An Taoiseach’s comments when this morning he confirmed that the shops will remain open and we have plans to ensure supply chains will not be interrupted."
Last week, large grocery retailers and retail distributors discussed their contingency plans with the Government.
The meeting was part of the work of the Cabinet subcommittee and ongoing engagement in relation to the virus.
Retailers and suppliers said they were continuing to work on their contingency plans.
Speaking after the meeting, Ms Humphreys said: "I am greatly encouraged by the preparations that retailers and suppliers are making to ensure that consumers have access to the range of grocery goods that they need.
"I am also assured that grocery supply chains are well stocked and there is ample supply to meet demand.
"Retailers and their suppliers are working on contingency plans and are following the public health advice provided by Government on a daily basis, so that health is prioritised for employees and consumers, and food supply chains can continue to function with minimal disruption."