Tosun posted a photo showing him and other Turkey internationals saluting fans in support of the Turkish army's offensive against the Kurdish-led Syrian Democratic Forces after the Euro 2020 qualifying win against Albania.
Tosun wrote on Instagram: "For our nation, especially for the ones who are risking their lives for our nation."
Several civilians and fighters have been killed in ongoing military actions and several European states, including Germany, have blocked sales to Turkey.
The Turkish Football Federation also posted an image on their Instagram showing players and staff saluting in the dressing room.
Although reports said UEFA will probe the incidents, European football's governing body told ESPN FC it could "not confirm" that because they had not yet received the match official's report from Friday's game.
Meanwhile, the salute and its digital imprint has led to more controversy in the Germany camp, just over a year after Mesut Ozil quit the national team after a heated debate over a picture showing the Arsenal star, Gundogan and Tosun with Turkish President Recep Tayyip Erdogan.
At the weekend, Tosun's post was liked by Germany internationals Gundogan and Can -- an action they quickly amended.
However, that was enough to stir up another debate over Germany national team players with Turkish backgrounds.
"I took the like back when I saw that it was judged to be political," Gundogan said in a statement published in parts by kicker. "Trust me: The last thing I wanted to do is make a political statement after what happened last year."
"What is true is that I was pleased for my former Germany U21 teammate that he scored the winning goal," Gundogan added.
Following the 3-0 win, he doubled down on his explanation and told reporters he had no "political intention" when liking Tosun's post.
Earlier, Can had told Bild that he unintentionally liked the post while scrolling through his timeline, and added he is against any war.
Both players were backed by Germany coach Joachim Low, who said postmatch that the likes were "in no case a political statement."
He added: "If you know those players, you'll know that they are against war and terror."
Germany general manager Oliver Bierhoff added: "Many players on this world liked that post. And you can't allege that all of them are in favour of war and terror."
Bundesliga 2 club FC St. Pauli, meanwhile, have released Turkish midfielder Cenk Sahin with immediate effect following an internal review.
On Friday, the 25-year-old former Turkey Under-21 international voiced sympathies with the Turkish army's military action in an Instagram story.
The club said they made their decision based on the player's "repeated disregard for the club values" but also to "protect the player."
They added: "Without any discussion and without any doubt we oppose acts of war. Those and solidarity for them fundamentally contradict the values of the club."