The IT problem - which has been described as a 'total outage' - led to the closure of all SPAR stores across the North of England yesterday (Sunday, December 5).
Lawrence Hunt & Co Ltd, which operates 25 branches across Lancashire, said the outage is affecting tills, credit cards and back office systems across the SPAR network.
The website for Preston food distributor James Hall and Co, which provides stock to hundreds of SPAR shops across the North, also remains offline today.
A spokesman for James Hall & Co said: "We are currently aware of an online attack on our IT systems. This has affected around 330 SPAR stores across the North of England over the past 24 hours and we are working to resolve this situation as quickly as possible.
"It is currently impacting stores’ ability to process card payments meaning that a number of SPAR stores are currently closed to shoppers or only taking cash payments.
"We apologise for the inconvenience this is causing our customers and we are working as quickly as possible to resolve the situation."
Some SPAR shops have confirmed they are back open, but shoppers can only pay with cash, whilst a number of stores remain closed.
This morning, the SPAR shop in Broadfield Drive, Leyland, said: "Our store is back open but we are operating cash only as our systems are still down. Thank you for all your ongoing support."
Yesterday evening (Sunday, December 5), Lawrence Hunt & Co said: "Unfortunately due to a total network outage affecting tills, credit cards and back office systems, it looks like we will remain closed for the whole of Sunday.
"Apologies from the whole of the Hunts team for the massive inconvenience to all our customers.
"We hope our partners will get us back up and running very soon."
Lawrence Hunt & Co Ltd have been approached for an update.