Sainsbury’s customers were unable to make contactless payments following an overnight software update and the firm was not able to fulfil the “vast majority” of online deliveries.
Meanwhile, Tesco had to cancel some online orders that were due for delivery.
Both chains apologised to customers and said they were working to solve the issues, which are not connected.
Sainsbury’s said in a statement: “Due to an error with an overnight software update, we are experiencing issues with contactless payments.
“All of our stores are open as usual today, accepting chip and pin and cash payments.
“Unfortunately, this also means we will not be able to deliver the vast majority of today’s Groceries Online orders and we are currently unable to contact customers directly, but will contact them as soon as we can to rebook orders.
“We apologise to customers for the inconvenience and are working hard to fix the issue.”
It later said the online ordering system was back up and running and that customers can place orders for delivery from Sunday.
One customer said she was meant to have a “very important” order delivered between 8-9am, which did not happen.
Yvonne, 56, from the Reading area, said: “The main issue I have with this is the poor communication from Sainsbury’s to its customers.
“It was obvious something was wrong at 7am as that’s when they send the receipts normally.
“Couldn’t get through to anyone about my 8 to 9 delivery.
“No statement until about 8.30, only seemed to be on social media which not all customers will have.
“Should have been an email or text to customers which would have helped those like myself expecting an early morning delivery. Much to improve on with their communications.”
Argos, which is owned by Sainsbury’s, has also been affected by the software update, meaning some customers may have had issues ordering new items or collecting orders in-store.
It said there may have been delays in fulfilling orders placed.
Only a small proportion of Tesco orders due for delivery on Saturday were impacted, it is understood.
Tesco customers received an email if their order was disrupted, and if it was cancelled they were not charged.
In-store shopping and placing orders on the app and website are not believed to have been affected.
Tesco said: “The vast majority of our online orders are being delivered as normal, but due to a technical issue earlier today we have had to cancel a small number of orders.
“We are contacting affected customers directly, and we’re really sorry for the inconvenience.”