The request was made in protest at legislation passed in Hungary.
Dieter Reiter had made the request in response to laws passed in Hungary, which ban the display and promotion of homosexuality to under-18s in the country.
UEFA declined it, and instead proposed alternative dates when the stadium could be illuminated.
Reiter criticised that decision, and also Germany’s football federation the DFB, and said city officials would now decide whether to illuminate other landmarks instead, including a wind turbine adjacent to the arena.
“I find it shameful that UEFA forbids us to send a message here in Munich for openness, tolerance, respect and solidarity with the LGBTQI + community,” he said in a statement.
“I am also very disappointed that the DFB (the German football federation), despite the unbelievably clear positioning here in Munich, in Bavaria and also in Germany, has not achieved or wanted to achieve anything.
“The alternative suggestion of illuminating the Allianz Arena on another day contradicts any message that is supposed to emanate from rainbow lighting.
“Tomorrow, as the city of Munich, we will still send a clear sign of our solidarity and our respect for sexual equality to Hungary and the world.
“We will not only fly rainbow flags at Munich town hall – I assume that the city council will decide this tomorrow with a large majority – but also make the wind turbine adjacent to the arena shine brightly and also the Munich Olympic Tower.
“Because we are concerned with a signal for a non-negotiable basic right for all people: equality and tolerance.”
Earlier, UEFA had released a statement which 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.”
UEFA proposed the Allianz Arena be lit up in rainbow colours on either June 28 – the Christopher Street Liberation Day – or between July 3 and 9 which is the Christopher Street Day week in Munich.
The decision on stadium illumination follows an announcement from UEFA on Sunday that Germany goalkeeper Manuel Neuer would not face action over a rainbow armband he wore during the 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 concluded there was no case to answer, given the 35-year-old was “promoting a good cause”.