The request was made by the mayor of Munich, Dieter Reiter, on Monday in response to a new law in Hungary that bans LGBT+ content in schools.
Because of that, the European football governing body said it "must decline" the request and instead proposed other dates for the stadium to be lit up in rainbow colours.
A statement by Uefa read: "Racism, homophobia, sexism, and all forms of discrimination are a stain on our societies – and represent one of the biggest problems faced by the game today.
“Discriminatory behaviour has marred both matches themselves and, outside the stadiums, the online discourse around the sport we love.
“However Uefa, through its statutes, is a politically and religiously neutral organisation. Given the political context of this specific request – a message aiming at a decision taken by the Hungarian national parliament – Uefa must decline this request.”
Germany are due to play Hungary on Wednesday in its final group stage game.
But Uefa suggested the Allianz Arena is lit up in rainbow colours on either June 28, Christopher Street Liberation Day, or between July 3 and 9, which is Christopher Street Day week in Munich.
The decision comes after Uefa on Sunday concluded Germany goalkeeper Manuel Neuer would not face action over a rainbow armband he wore during games against France and Portugal.
Neuer wore the armband to show his support for the LGBTQ+ community during Pride Month, prompting Uefa to investigate whether it could be viewed as a political statement.
But Uefa said there was no case to answer as the goalkeeper was “promoting a good cause”.