The store in Bletchley was affected by a problem with the company's card payment system.
Long queues formed at Asda check-outs after customers across the UK were unable to pay with their cards.
Shoppers described the technical issue as a "fiasco", and said it had led to "chaos" at supermarkets.
The company said all of its 626 UK stores were affected "at one point or another" during the day by the problem with its card payment system.
A spokesman said: "We are in the process of resolving a technical issue with our card payment system in stores.
"We're continuing to process payments as quickly as we can but apologise to our customers for the inconvenience this has caused."
A statement later said the majority of its stores were "working normally again".
Asda had earlier tweeted: "We're aware of an issue with our store's accepting card payments & are working to fix it asap, we're sorry for any inconvenience caused."
MKFM listeners told us
Sarah Rolls, I was there around 11ish. Abandoned trolleys everywhere. Queue past the entrance of Asda Bletchley for the cash points. Complete chaos. Lots of angry customers and flustered staff. Just as we were leaving they were bringing out the old credit card swipe machines where yo have to put the card on the thing and swipe across the paper slip.
Lesley Billington, I was there at 1ish...one lady at doorway telling people no card payments ...there was no announcements over the loud speakers...huge queues yet there was checkouts closed...surely they should have all been open?
Stuart Masterton, I wouldn't go as far as to say "complete chaos" but there were a number of people who either didn't understand English or weren't paying attention to the announcements as they got to checkpoint trying to pay by card only to be told cash only. Asda is always chaos on a Sunday. I only go there for the pizza.
Sue Sibbert, I went yesterday around 1ish not knowing of the fiasco. There were only two members of staff out the entrance advising of the problem. Member of staff told me I queued up to withdraw cash. Inside shop was lots of frustrated customers and staff!! Abandoned trollies everywhere. Only heard one announcement made when I was there advising of card machine problem. I do feel the staff were doing their best it wasn't their fault card machines were down.
Laura Alana Arthur, Just an example of how the world can't seem to cope when technology fails. Then people act like CASH is a foreign word and panic. The store should have had a better emergency plan of action by the sound of things, though.
Cheryl R Brooks, Wasn't like that in Wolverton. They handled it brilliantly, even handed out chocolates because we did have to a little longer than usual.
Stephen Burroughs, Man on the door was trying to tell everyone. I went in had cash on me already so no dramas. Lots of people getting angry at staff. Not their fault, though, there was a tannoy announcement while I was in there. Yes communication could have been better but I think they were trying to keep all the tills open with cash which isn't easy.
Gary West Very poor communication from the store. Apparently, there was a member of staff at the entrance telling people about the fault but when I came into the store I didn't see them. First I heard about it was a staff member shouting at the tills. A few notices at the doors and use of the tannoy might have saved a lot of hassle.
There were reports that some Asda stores, including one at Reading in Berkshire, had been closed.
Twitter user Si20100 messaged the company saying: "Hi had to use voucher in asda today they couldnt tell me how long to process payment..was a fiasco tbh how long pls?"
Another shopper, writing on Twitter as Charstuart97, said the Asda store in Reading had been closed and posted a picture from inside her car where she said she could not leave the car park due to queues of vehicles.
Twitter user Nateeatschicken wrote: "There is mass confusion at the Scan & Go area. Stood there for 30-40 mins only to be told it is cash only."
ClaireWilliam10 tweeted: "Asda aberdare is CASH ONLY today. Problem with the card readers. If your going shopping there make sure you have the cash before shopping."
And DaveCthetrucker wrote: "How much has @asda lost today then? Went into my local, it was CHAOS, went to Morrisons."
Original article by Sky News