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).