O2 customers were the first to have access at 10:00 GMT, but some reported problems with its app and website.
Those who did manage to purchase tickets reported prices ranging from £56 to £199, with VIP "on stage" seats at a wallet-busting £1,950 to £2,390.
There will be further pre-sales on Friday and Monday.
Tickets for the pop superstar's five UK stadium shows in Cardiff, Edinburgh, Sunderland and London will then go on general sale on Tuesday.
The UK concerts are part of a 43-date world tour in support of her Grammy-nominated Renaissance album.
The shows kick off in Sweden on 10 May, before landing at Cardiff's Principality Stadium a week later.
She will then visit Edinburgh's Murrayfield on 20 May, Sunderland's Stadium of Light on 23 May and London's Tottenham Hotspur Stadium on 29 and 30 May.
Beyoncé has set the standard ticket prices at roughly the same level as her last stadium tour, with her husband Jay-Z in 2018, when entry started at £51.
However, the VIP packages, some of which included guaranteed front row seats, are more than four times that tour's top price of £475.
Many fans on social media ridiculed the cost, reminding Beyoncé that she advised people to "quit their jobs" on her recent single, Break My Soul.
Billboard magazine predicted the five-month tour could earn the star up to $275m (£223m).
The phrase "O2 Priority" trended on Twitter after the company's app and website fell over ahead of Beyoncé's ticket sale.
Hundreds of fans were upset that they couldn't access the site, but others were more concerned that they'd missed out on a free coffee from Greggs.
In a statement, the company apologised "to anyone experiencing difficulties".
"Tickets are selling and we're seeing huge demand. We're doing everything we can behind the scenes to help keep the app running smoothly."
The O2 app and website also crashed when the company had pre-sale access for another major tour, for comedian Peter Kay, in November.
In North America, Beyoncé fans are being asked to register for Ticketmaster's Verified Fan process - which the company says will filter out touts - before ticket pre-sales open on Monday.
Those who have registered will be entered into a "lottery-style process" if demand outstrips the number of available tickets.
Politicians in the US, who are already investigating Ticketmaster over the fumbled sale of Taylor Swift's Eras tour, will be keeping an eagle eye on how the systems cope with Beyoncé's concerts.
Frankie Austick, 19, secured his tickets though the O2 Priority website after his app crashed.
"It's such a nerve-wracking experience, such a nail-biting one, but so worth it in the end," he told BBC Radio 1's Newsbeat.
"To have got through, to have got to the front of the queue, to have got the tickets, it's just so amazing."
Frankie, who is from Durham, paid £59 for his ticket and said he was "so happy to be seeing her in Sunderland of all places".
"I have lived in the north east for my whole life and to see such a big artist giving us the support that we need... for so many people it will be the only chance to see her, when she comes locally."
After waiting over an hour in Ticketmaster's virtual queue, Katie Battersby made it to the booking page only to be taken all the way back to the start with 138,000 people ahead of her.
Katie, 25, recorded her experience for Newsbeat, saying that she, like so many, tried to go to the O2 priority website again.
"And it completely crashed. I have had two friends who have got to this page and they have been kicked out of the queue."
In spite of today's disappointment and frustration, Katie is determined to get her tickets.
"We will be back tomorrow to try again."
Beyoncé's last outing as a solo artist was 2016's Formation tour, which saw the star perform in front of a 60ft LED cube called the "monolith".
She then staged a joint tour with Jay-Z, in which the couple re-enacted their estrangement and reconciliation every night, in a two-and-a-half hour musical melodrama.
Last week, the star performed her first headlining concert in four years at the opening of a luxury hotel in Dubai, but did not play any of her new material.
She was reportedly paid $24m (£19.4m) for the one-off show, but faced criticism for performing in a country where homosexuality and gender reassignment are outlawed.
Critics said that contradicted the message of her latest album, which explicitly celebrates black and queer dance culture.
Beyoncé conceived the Renaissance album as "a place to dream and to find escape" during the pandemic, layering her songs with multiple samples and references to club music, from Nile Rodgers' Studio 54 disco grooves and Grace Jones' imperious soul, to less-celebrated movements like bounce and dancehall.
Exclaim magazine called it "the sound of a once-in-a-generation superstar performing at her peak", while the Guardian described it as "a breath-taking, maximalist tour de force".
Unusually, Beyoncé has avoided making music videos for the album, meaning the Renaissance tour will be fans' first chance to see her visual interpretation of tracks like Break My Soul, Alien Superstar and Cuff It.
The star generally reworks and updates old songs to fit her current aesthetic, so we may also hear clubbed-up remixes of hits like Crazy In Love, Formation and Single Ladies.
The former Destiny's Child star may reveal further details at this weekend's Grammys, where she is up for nine awards, including album of the year.