Demiral scored both of Turkey's goals in the 2-1 last-16 win over Austria on Tuesday and during celebrations for his second goal made a gesture associated with Turkish right-wing extremist group Grey Wolves.
UEFA said in a statement Demiral was banned "for violating the basic rules of decent conduct, for using sports events for manifestations of a non-sporting nature and for bringing the sport of football into disrepute."
Demiral will also miss a potential semi-final against England or Switzerland should Turkey overcome the Netherlands on Saturday.
Turkish President Recep Tayyip Erdogan will attend the quarter-final at the Olympiastadion in Berlin after Demiral's salute triggered a diplomatic row between Turkey and Euro 2024 host nation Germany.
Turkey summoned the German ambassador on Wednesday over politicians' reactions to Demiral's celebration.
Germany's Interior Minister Nancy Faeser warned "the symbols of Turkish right-wing extremists have no place in our stadiums".
While Erdogan himself has not yet weighed in on the row directly, several ministers and the spokesman of his ruling AKP party have condemned Faeser's reaction.
Demiral said his celebration was related to his "Turkish identity".
The 26-year-old former Juventus defender, now at Al-Ahli in Saudi Arabia, said there was no "hidden message" in his gesture.
Demiral posted a photo of his celebration on X with the caption "How happy is the one who says 'I am a Turk'."
The Grey Wolves advocated radical ideas and used violence in the 1980s against leftist activists and ethnic minorities.
The group has been banned in Austria and France but not in Germany.
Germany's agriculture minister Cem Ozdemir said Wednesday "nothing about the wolf salute is hidden".
Ozdemir, one of the most prominent German politicians with Turkish roots, said the symbol "stands for terror (and) fascism".
The Grey Wolves were labelled "a terrorist organisation" by the European Parliament in 2021 and "especially threatening for people with a Kurdish, Armenian, or Greek background and anyone they consider an opponent".
Accusing German authorities of "xenophobia", Turkey's foreign ministry pointed out that Germany's domestic intelligence service had emphasised in its report "not every person making the grey wolf sign can be described as a far-right extremist".
Demiral's double helped Turkey reach the last eight of a major tournament for the first time since 2008.
With an estimated three million Turks living in Germany, the team has enjoyed heavy backing across the country for its Euro 2024 matches.
Berlin police have said they will deploy more officers than usual for Saturday's quarter-final, which is considered a "high-risk game".
Germany's capital is home to the largest Turkish community outside of Turkey, many of them the descendants of "guest workers" invited under a massive economic programme in the 1960s and 70s.
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