Fans buying tickets for Adele's tour have told the BBC they were shown the address and credit card details of customers other than themselves.
Advance tickets were made available to members of Adele.com this morning.
But several fans said they saw other people's shopping baskets, including payment details, upon check out.
Ticketing company Songkick said due to the "extreme load" on the site some customers could see others' account details. It apologised for any "alarm".
"At no time was anyone able to access another person's password, nor their payment or credit card details (which are not retained by Songkick)," it said.
Kiran Farmah, in Birmingham, said she was offered tickets for Glasgow shows.
"I got through to buying tickets but it came up with someone else's screen with their card details and home address for SSE," she tweeted.
Emma Harris in Woking told the BBC she had experienced a similar problem.
"After queuing for an hour and half, we clicked the tickets we wanted [and] got pushed through to another screen but different tickets were selected."
"We went with these anyway because we thought otherwise we'd lose out. But when we got to the next screen, where you fill in your details, all of the boxes were already filled in with somebody else's name, somebody else's address and somebody else's credit card number."
Harris said she deleted the other customer's "big, long digit card number" and eventually obtained tickets for the O2 in London next March.
"It's definitely worrying, as I know myself and a lot of friends of mine have paid with our credit card details and we don't know who they've been exposed to."
The sale was organised by live music and technology firm Songkick, which provides concert tickets and allows fans to be alerted to upcoming shows.
"Due to extreme load experienced this morning, some of our customers were incorrectly able to preview limited account information belonging to other customers...
"We take the security of our users and Adele's fans very seriously, and we apologize for the alarm we have caused to those purchasers who experienced issues."
Security consultant Graham Cluely said the incident "certainly sounded" like a security breach.
"This is the sort of thing which should be impossible, even if the website is very busy," he told the BBC.
"It sounds like the website [code] has been written insecurely. It's spitting out other people's information - information which they would expect to have been kept private."
He agreed it was still "unclear" whether credit card numbers had been exposed, but urged customers to be cautious.
"If that information could have been exposed, then keep a close eye on your bank account and your credit card statements. Look for unusual activity there and be very wary of unsolicited messages or unusual emails which you might receive."
My experience - Ian Youngs, BBC entertainment reporter
After dutifully signing up to Adele's website to be eligible for the presale like countless others, and logging on at 08:57, and being in a queue on the website - unexpected euphoria. I'm in.
I select two tickets at £55 each for one of the Manchester dates. But on the next screen, I'm informed I've selected four tickets at £95 each. Clearly something has gone wrong.
The clock ticking, a snap decision is required. How much do I like her? Enough to spend £380 (plus fees) rather than £110? Sorry Adele - I remove the tickets in the hope I can choose different ones.
But no - I'm just thrown out of the booking process and shoved to the back of the queue. At the time of writing, an hour and a half later, I'm still in the queue and the site says tickets are "still available". I suspect they've realised there's a gremlin in the system.
The tour kicks off in Belfast on 29 February and finishes in Antwerp on 13 June next year. It also includes four dates at London's O2 Arena.
It will be the first time Adele has toured since 2011. That tour ended prematurely due to the discovery of a haemorrhage on her vocal cord, which required surgery.
With huge demand for her new gig tickets, Adele's website carries a request that purchasers do not sell tickets on for a profit.
Reselling tickets at inflated prices is common for sold-out gigs and is not illegal in the UK. But it often causes consternation among genuine fans and the site says: "The resale of tickets will not be tolerated."
However, dozens of tickets for the singer's shows have already appeared on secondary ticketing sites.
Viagogo is offering a single ticket to London's O2 Arena for £3,506. On Get Me In, the top price is £770.
Coldplay recently signed an open letter to the government calling for action over secondary ticketing sites, saying fans are being "ripped-off by touts who anonymously exploit fair ticket prices via online ticket marketplaces".
Songkick said there had only been a "low level" of ticket resale for Adele's show, suggesting that just 2% of the 57,000 tickets sold on Tuesday morning had found their way onto secondary sites.
"Compared to other events, we believe these efforts helped to reduce resale by well over 50%, increasing the amount of fans that can attend these shows," it added.