Former Wales team captain Laura McAllister, who is an ambassador for her country at the tournament, was among a number of supporters told to remove the hats.
Some have claimed they were told it was a “banned symbol” despite Fifa previously saying rainbow coloured flags and clothing were not prohibited in the stadiums.
Same-sex relationships are outlawed in the Gulf state but the host nation’s organisers had repeatedly said “all are welcome” in the run-up to the competition.
Asked about the incident, the Prime Minister’s official spokesman said: “Obviously it’s not the approach that this Government would take if we were hosting any tournament.
“LGBT rights are a fundamental part of the United Kingdom.
“We have raised concerns about LGBT visitors with the Qatari authorities at all levels leading up to the tournament and obviously we will continue to monitor it carefully.”
He added: “We will monitor carefully UK fans in the region and how they are treated and obviously people are going there to enjoy a football tournament, first and foremost, and we are confident that’s what the Qataris will want to be focused on as well, facilitating people supporting their teams.”
The Football Association of Wales (FAW) said they were “extremely disappointed” in the actions of staff at Ahmad bin Ali Stadium towards fans, revealing members of the FAW team were among those asked to take off their hats.
In the statement, the FAW said they were collecting information on the alleged incidents and would be addressing them directly with Fifa on Tuesday.
News that fans wearing rainbow garments were denied entry to the stadium and asked to place items into lost property has sparked outrage.
I think we’ve had plenty of warning that this wasn’t going to be a World Cup where human rights and LGBT rights and women’s rights were well respected really
Ms McAllister said she was furious at being told to take her hat off but told ITV it was important to “stick to our values”.
“I think we’ve had plenty of warning that this wasn’t going to be a World Cup where human rights and LGBT rights and women’s rights were well respected really,” she said.
“But coming from a nation like Wales, we were very keen that we still took a stand.”
The PA news agency was made aware of at least one male Wales fan who was told to take off his bucket hat off leaving him “upset and angry”.
It has been reported US sports journalist Grant Wahl was also barred from the game for wearing a rainbow T-shirt unless he changed.
When you think that Fifa and Qatar couldn't get it any more wrong, they do something like this
Tim Hartley, Wales fan and head of fan charity Gol Cymru, told PA: “This whole tournament leaves a nasty taste in the mouth.
“When you think that Fifa and Qatar couldn’t get it any more wrong, they do something like this.”
Some fans have claimed they were told the rainbow coloured items were being confiscated for their own safety.
A PA journalist witnessed a US fan being threatened for carrying a miniature rainbow flag on the Metro journeying to the Wales match by a man who appeared to be a Qatar supporter.
The man threatened to “kill” the fan and said “that flag is banned in this country”.
Wales and US fans had to intervene to diffuse the situation.
Despite this, former England footballer and BBC pundit Alex Scott wore the armband during a live broadcast from the England match against Iran.
Wales fans have also complained that a number of their large banners and flags were confiscated heading into the stadium, despite pre-registering them weeks in advance, as is required by Fifa.
Some of those who were told to place their flags into storage have reported that their banners were missing at the end of the game, and have appealed on social media to find them.