Social media users say their discounts are not working at the till, with one person posting a photo of an error message at the self-checkout, which reads: "We are really sorry some promotions and discounts are not working at this time."
The Morrisons website was also down for a period in the morning, with error messages on some pages suggesting invalid or late responses from servers.
It now appears to be back up and running.
Morrisons had been advertising large discounts ahead of Christmas, including some vegetables for 10p.
"There's never a good time for a tech glitch, but for it to happen on what is expected to be the busiest day of the year is the stuff of nightmares," says retail analyst Natalie Berg.
"This will further erode shopper trust and impact profitability.
"Supermarket margins are razor-thin to begin with and this Christmas has been especially promotional," adds Ms Berg.
"This problem just shows how reliant supermarkets are on their systems to ensure that the millions of shoppers who shop with them have seamless experience," says Catherine Shuttleworth, retail analyst at Savvy Marketing.
"A systems glitch like this couldn't come on a worse day," she adds.
Today is predicted to be the busiest shopping day for supermarkets this year, according to retail analysts Kantar.
Sales at supermarkets are expected to reach over £13bn for the first December ever.
Morrisons is the fifth-largest market supermarket in the UK, according to Kantar, with 8.6% of the grocery market in the 12 weeks leading up to 1 December 2024.
"Retailers are putting more and more deals through their loyalty cards and if shoppers can't access them, they will feel cheated," said Ronan Hegarty, news editor of trade publication The Grocer.
"That it has happened so close to Christmas will leave a bad taste in customers mouths and have them thinking about where to shop next."