Reiter had said he wanted to light up the stadium in the colours in protest against a new law in Hungary that bans the dissemination of content in schools deemed to promote homosexuality and gender change.
On that basis, UEFA said it could not grant the request and proposed alternative dates for the stadium to be lit up in rainbow colours.
A statement from European football's governing body read: "UEFA has yesterday received a request from the mayor of Munich, Dieter Reiter, on behalf of the city council, to have the arena in Munich illuminated in rainbow colours at the upcoming UEFA EURO 2020 group stage match between Germany and Hungary.
"In this letter, the mayor outlines the reasoning behind this request to be a political decision which has been taken by the Hungarian parliament.
"UEFA understands that the intention is also to send a message to promote diversity and inclusion - a cause, which UEFA has been supporting for many years having joined forces with European clubs, national teams and their players, launching campaigns and plenty of activities all over Europe to promote the ethos that football should be open to everyone and consequently UEFA has proposed alternative dates for the illumination which align better with existing events.
"UEFA is determined to play its part in positive change and believes that discrimination can only be fought in close collaboration with others
Sign for an Equal Game forms the latest instalment of the Equal Game campaign, which has run for the past four seasons and which aims to create positive social impact under UEFA's overarching value of Respect. Its main purpose is to make people aware that football is for everyone, no matter who they are, where they are from and how they play.
"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.