Culture Secretary Michelle Donelan has said she would wear the OneLove armband if she was to attend the World Cup in Qatar.
Football’s governing body prompted anger by preventing the captains of seven European nations taking to the pitch with the armbands on, by threatening to issue yellow cards to players who defied the ruling.
Ms Donelan said she “100 per cent” backs Mr Andrew for wearing the armband.
“I support the campaign behind… and the sentiment behind the OneLove armband and I believe in us being able to stand up for our values and I’m proud that he’s going to wear that,” she told Sky News.
Asked if she would too, she said: “Yes, I think I would actually.”
Senior political figures from Germany, Belgium and Denmark have worn them in protest while watching on from the stands.
Mr Andrew, the UK’s first openly gay sports minister, will follow suit, the Department for Culture, Media and Sport has confirmed.
He accused Fifa of putting players in an “impossible position” and said the organisation had “serious questions to answer” about its stance.
“Two weeks ago they wrote to everybody to say just concentrate on the football and don’t do the politics,” he told the Standard. “Then they say you can’t wear the armband, but you can wear ours. I’m sorry, that is just not an acceptable position.”
Mr Andrew also added his voice to calls for countries’ human rights records to be taken into account when hosts are chosen for World Cup competitions.
“There is a spotlight on Qatar now and that is a spotlight that we should not let go out as soon as the tournament is over,” he said. “I really hope that Fifa will have a long hard look at the criteria that are needed for host nations to host such tournaments.
“Clearly, I would have thought their ambition would be for everybody to want to enjoy the games and make them the most successful ever.”
Fifa banned OneLove armbands on the eve of the tournament, citing rules on “political, religious or personal messages or slogans”.
The organisation brought forward its own awareness campaign and said captains could wear an armband bearing the words: “No Discrimination”.