The third game of that three-match ruling will be suspended for a probationary period of two years, while the Hungarian Football Federation have also been fined €100,000.
Uefa have also ordered that a banner with the message “#EqualGame” and featuring the Uefa logo on it be displayed during those next two matches in Budapest.
Uefa’s ruling - which does not apply to 2022 World Cup qualifiers, which fall under Fifa’s remit - comes after they appointed an ethics and disciplinary inspector to investigate “potential discriminatory incidents” during the 2-2 Group F draw with Hungary in Munich on June 23.
European football’s governing body had already opened an investigation into Hungary’s matches against Portugal and France in Budapest.
During the opener against Portugal, images on social media showed banners among some fans at the Puskas Arena that had “Anti-LMBTQ” on them - the Hungarian abbreviation for Lesbian, Gay, Bisexual, Transgender and Queer.
Ahead of Hungary’s second Group F contest against France, some Hungarian supporters marched to the Puskas Arena carrying a banner that called on players to stop taking a knee to protest against racism.
Uefa later declined a request to illuminate Munich's Allianz Arena in rainbow colours for Hungary’s match against Germany on the grounds of the gesture having political context.
European football's governing body said it received the request from the mayor of the German city, Dieter Reiter. Uefa said that the mayor's reason for the request was a response to legislation passed in Hungary banning gay people from appearing in school educational materials or programmes for under-18s.
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. Reiter later called the ruling "shameful".
Hungary are due to host European Championship finalists England in World Cup qualifying in Budapest in September.
Additional reporting by the Press Association.