The Ayrshire band announced plans to play three nights at the Glasgow Barrowland earlier this week.
The special shows on December 5, 6 and 7 will gives fans the chance to choose the band's setlist, with each night focused around a different pair of albums from their back catalogue.
Fan Ruth Hill tweeted: "Biffy Clyro tickets sold out by 1 minute past 9?! I remember the days when you could see them hassle free for a tenner in Dunfermline!"
Martin McGuire tweeted: "I set an alarm for 9am and everything to get up for these,never stood a chance. Sad little old me :("
Blair Rankin tweeted: "Was there right on 9:00 am for @BiffyClyro tickets but naw, ticketmaster clearly doesn't like me."
The band had implemented additional measures including putting names on tickets and offering a larger percentage of tickets to members of their fan club in a bid to reduce the chance of touts getting the tickets.
They are now asking any fans who see tickets for the shows being sold online to contact them at email@example.com
In a statement, the band said: "Tickets for all three nights of Biffy Clyro at Glasgow Barrowland have now sold out.
"While many of you will be delighted to have bought tickets to see the band in December, we are also acutely aware that many of you will be very disappointed not to have been able to purchase tickets for the shows.
"Due to unique fan-centric nature of these shows, we have done everything in our power, whilst planning these events, to try and manage this in an appropriate way, and to not treat these like our other shows. In some cases, this may have seemed slightly awkward, but we truly believe that this all contributed to ensuring the event was available to our fans, both first and foremost.
"We have introduced names on tickets, limited the amount you can buy, checks on the door and offered TEAM BIFFY members a larger percentage of pre-sale tickets compared to the general sale. "All of this was in the hope that as well as prioritising our fans, we have reduced the chance that any of these tickets would make their way into the hands of touts. We teased the shows on the days prior, dropping small, timed hints that we thought might engage only the fans, without alerting the touts.
"The Barrowland holds a special place in the bands heart and fits perfectly with the unique nature of the shows, sadly however it can't hold everyone who we know would like to go to these shows.
"We hope those that are disappointed today, understand and realize that we have done and will continue to do everything within our power to make sure there's not a single tout outside any of the three nights, and that you can take some consolation knowing that hopefully every single ticket for this event, was purchased by a fellow fan of the band, in a fair manner."