Sainsbury's has suspended its online grocery service, meaning thousands of customers will not receive their orders on Wednesday and Thursday.
The company said a computer fault was spotted on Tuesday and it has been ringing people who booked a delivery to offer them £10 in compensation.
The supermarket giant says it is doing all it can to resume normal service.
It has apologised to customers, who see a fault message when they try to make orders online.
Sainsbury's said it had contacted the majority of customers who were expecting a Wednesday delivery to advise them of the problem by mid-morning.
Compensation voucher
A company spokesman said: "We froze our online home delivery website late yesterday [Tuesday] afternoon when we identified a technical issue and we are contacting customers whose deliveries have been impacted.
"We apologise for any inconvenience this may cause."
The supermarket said this evening that it could give no definite time at which normal deliveries would resume.
Those affected will be compensated with a £10 voucher which they can use towards their online shopping with the supermarket.
The technical problem means the company is unable to access customers' orders.
Sainsbury's stressed there was no suggestion that people's personal details were at risk.
One customer, Bridget Hoad from Grantham, Lincolnshire, was due to have her family's £140 weekly shop delivered in a one-hour time-slot from 1000 BST on Wednesday.
She only found out there was a problem about 15 minutes after the delivery window had started.
"I was initially very angry but if it's a technical glitch, that's beyond their control. But I would have appreciated being contacted earlier. It's inconvenient and frustrating," she told the BBC News website.
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