Neuer has worn the armband during Germany's last two Euro 2020 fixtures to show support for the LGBT+ community during Pride Month, but UEFA launched an investigation to determine whether it could be viewed as a political statement.
Had UEFA determined that the armband was a political statement, Neuer could have been prohibited from wearing it in future games and the German FA (DFB) could have faced a fine for the goalkeeper’s actions.
The DFB announced on Sunday evening that UEFA had dropped its probe and now views the armband as a "good cause", though European football’s governing body is facing criticism for its decision to launch an investigation in the first place.
A DFB statement read: "UEFA have today shared with the DFB that they have stopped the review of the rainbow captain's armband worn by @Manuel_Neuer.
"In a letter, the armband has been assessed as a team symbol for diversity and thus for a 'good cause.'"
The DFB says Neuer wears the armband as a symbol of “the whole team’s clear commitment to diversity, openness, tolerance and against hatred and exclusion.”
Ahead of Germany’s final group game against Hungary on Wednesday, the Mayor of Munich will ask permission from UEFA for the Allianz Arena to be lit up in rainbow colours.
Mayor Dieter Reiter said on Sunday he was going to write to UEFA to ask for the stadium - the home of Bayern Munich and the national team - to be lit up with the colors as a sign against homophobia and intolerance when they play Hungary.
"This is an important sign of tolerance and equality," Reiter told news agency dpa.
Munich's city council had already called for the stadium to be lit in rainbow colors for the final Euro 2020 group game to protest a law passed by Hungarian lawmakers on Tuesday that prohibits sharing with minors any content portraying homosexuality or sex reassignment. The law has been denounced as anti-LGBT discrimination by human rights groups.
The Munich city council accused Hungary "of following the example of Russia's homophobic and transphobic legislation."
Meanwhile, UEFA has launched an investigation into “potential discriminatory incidents” during Hungary’s group matches.
The incidents are alleged to have taken place during Hungary’s opening 3-0 Group F defeat to Portugal on Tuesday and Saturday’s 1-1 draw against France.
Hungary fans carried an anti-kneeling protest banner as they marched to the stadium for Saturday’s game and other banners saying ‘Brotherhood’ and ‘Magyarorszag (Hungary)’.
The country’s prime minister Viktor Orban has said he supported the anti-kneeling protests and that “this kneeling business” should not take place on the pitch.
Hungary sit bottom of Group F but can still qualify for the knockout stages if they beat Germany on Wednesday.
Additional reporting by PA.