Kevin Davies, understood to be from Pembrokeshire, is reported to have been rushed to Hamad General Hospital, in Doha, following Wales’ match against Iran, where he later died.
It is understood to have been a medical incident and that he did not attend the 2-0 defeat but instead remained at his apartment after feeling ill.
Football Supporters Association Cymru’s Paul Corkrey told the PA news agency: “He was part of the Red Wall and we’re all devastated for him and his family.
“We’re all like one big family and we lost one of our family members today.”
Mr Corkrey also paid tribute to Mr Davies’s son and friends, saying they had been very “brave” in the way they had handled the situation.
The British Embassy, Qatari authorities and the Football Association of Wales (FAW), as well as travel company Wonky Sheep, are said to be helping the man’s son to make all the necessary preparations and fly home.
“Everyone has been very helpful, and everyone who has been asked for help has come through,” Mr Corkrey added.
A Foreign, Commonwealth and Development Office (FCDO) spokesman said: “We are supporting the family of a British man who has died in Qatar.”
Noel Mooney, chief executive of the Football Association of Wales (FAW), added on Twitter: “So sorry to hear that one of our supporters has passed away here.”
He added: “Our condolences go to the family and of course we are here to support however we can.”
The FAW said in a statement: “Mae CBDC yn cydymdeimlo efo teulu a ffrindiau Kevin Davies.
“Our deepest condolences from everyone at the Football Association of Wales. Our thoughts are with Kevin’s family and friends at this sad time.
“The FAW is in contact with Kevin’s family to help in whatever way we can.”
Officials believe more than 2,500 Wales fans have made the trip to Qatar for the tournament.
Their numbers have been bolstered by fans already in the region arriving on shuttle flights to watch Wales take part in a World Cup for the first time since 1958.