The defender raised both hands and made the gesture with his fingers after his second goal in Turkey's stunning 2-1 win over Austria in the last-16 of EURO 2024.
The gesture - mimicking the shape of a wolf's head - is linked to the right-wing "Grey Wolves", an ultra-nationalist youth branch of Turkey's Nationalist Movement Party (MHP), which is in alliance with President Tayyip Erdogan's ruling AK Party.
"The symbols of Turkish right-wing extremists have no place in our stadiums," Germany's Interior Minister Nancy Faeser said in a post on X. "Using the European Football Championship as a platform for racism is completely unacceptable."
Established in the 1960s, the "Grey Wolves" were involved in political violence between leftists and nationalists that killed some 5,000 people around the time of a 1980 coup.
The group is outlawed in France and, according to media, its symbol is banned in Austria. The "Grey Wolves" are also under surveillance in Germany, Faeser added.
UEFA said it would look into "the alleged inappropriate behaviour" of Demiral.
It has been cracking down on misconduct during the tournament, banning Albania's Mirlind Daku for two games after he led fans in offensive chants, and investigating England's Jude Bellingham for a crotch-grabbing gesture.
Turkey's foreign ministry said UEFA's probe was unacceptable and that German authorities' approach to Demiral "involved xenophobia".
"We condemn the politically-motivated reactions to the use of a historical and cultural symbol, in a way that does not target anyone, during the celebrations of joy at a sporting event," it said.
The ministry also summoned Germany's ambassador to Ankara over the dispute, a Turkish diplomatic source said.
'Proud to be Turkish'
Elated by his man-of-the-match performance, Demiral told reporters he had planned the gesture.
"I had a certain specific celebration in my mind. That's what I did. It has to do with Turkish identity because I'm very proud to be a Turk," he said in UEFA's translation of his comments in Turkish.
"I'm very happy that I did and all of our fans are proud of us. And I saw people in the stadium who were doing that sign, so that reminded me that I also had that in mind. So I'm happy I did that."
The German Israeli Society, which described the Grey Wolves as a threat to Jews as well as Armenians, Greeks and Kurds, called on German authorities to ban the group.
"The ideological superiority of these fascist nationalists jeopardises public safety," its president Volker Beck said in a statement.
In Turkey, the ruling AK party and its MHP ally both defended Demiral and said the backlash was out of proportion.
"There's no need to write at length (about this)..." Bak wrote on X above a photo of Demiral making the gesture.
Nationalist Movement Party leader Devlet Bahceli went further, however, lambasting the UEFA probe.
"The Grey Wolf sign made by our son Merih after hitting the net is the Turkish nation's message to the world, and UEFA's launch of an investigation in this context is both ill-intentioned and part of a chain of provocations that have gained dangerous ground in recent days," he said.
The incident coincided with the start of a trial in Turkey of 22 people over the murder of former "Grey Wolves" leader Sinan Ates, who was gunned down in Ankara in late 2022.