UEFA were investigating whether this contravened their rules over athletes not being permitted to make political statements. But UEFA said Sunday in a statement Neuer was "promoting a good cause" and opted against pursuing any further action.
"UEFA have today shared with the DFB that they have stopped the review of the rainbow captain's armband worn by Manuel Neuer," the German Football Association said on Twitter. "In a letter, the armband has been assessed as a team symbol for diversity and thus for a 'good cause'."
Germany face Hungary in their final Group F group match on Wednesday and Munich mayor Dieter Reiter said on Sunday he was going to write to UEFA to ask permission to light up the Allianz Arena in Munich with rainbow colours.
"This is an important sign of tolerance and equality,'' Reiter told news agency dpa.
"It is important for the state capital Munich to set a visible sign of solidarity with the LGBTI community in Hungary, which is suffering from the current stricter homophobic and transphobic legislation of the Hungarian government,'' the Munich council said in its application.
UEFA is investigating "potential discriminatory incidents" during Hungary's European Championship matches against Portugal and France at the Puskas Arena in Budapest, European football's governing body said on Sunday.
During Hungary's opening match against Portugal on Tuesday, images on social media showed banners with "Anti-LMBTQ" on them -- the Hungarian abbreviation for lesbian, gay, bisexual, transgender and queer.
Hungary's parliament passed legislation last week that bans the dissemination in schools of content deemed to promote homosexuality and gender change, amid strong criticism from human rights groups and opposition parties.