Twin brothers Matt and Luke Goss - who enjoyed a major hit with the track When Will I Be Famous? - cancelled August shows in Newcastle, Glasgow, Birmingham and Nottingham.
The band will still play two shows at London's O2 Arena - one of which sold out in a record seven seconds - and another in Manchester on August 22.
In a statement, the band apologised and said the shows were cancelled due to "logistical circumstances beyond their control".
Fans aired their disappointment on social media and speculated there had been poor ticket sales at the cancelled concerts.
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Elle Marwick wrote on Twitter: "So , so disappointed Bros will not be returning to Glasgow . 'Logistical Difficulties'? Hmmmm .You were my very first gig ever .Gutted."
Stephen Spence posted that he was "absolutely devastated" to miss the reunion tour, while Daz Gale said: "logistically nobody bought tickets".
Darryl Ashton wrote: "Bros have cancelled all concerts outside #London and #Manchester."Due to unforeseen 'logistical" circumstances'. Poor ticket sales."
Matthew Borland added: "Logistical circumstances" also known as zero ticket sales."
Before the four other dates were cancelled, there were still tickets available for the second London show and the one in Manchester.
In a statement, they said: "Due to logistical circumstances beyond their control, it is with sincere regret that Bros have been forced to cancel four dates on their forthcoming UK tour.
"Matt and Luke Goss apologise to their fans for any disappointment."
They added that ticket holders from the cancelled dates will be refunded.
In their heyday, Bros inspired teenagers to wear bottle caps on their shoes.
They last played together in 1989 and split in 1992.