The Everton striker had to be restrained at times by team-mates as he got involved in a heated exchange with someone in the stands near the halfway line and was eventually shown a red card by the referee, the first of his career.
According to the Turkish Football Twitter account, Tosun reacted angrily when a projectile or flare was thrown towards where his father and uncle were sitting in the stands at the Stade de Geneve in Switzerland.
The score was 1-1 at the time and the match eventually ended 2-2 thanks to Caglar Soyuncu's injury-time equaliser.
Tosun issued an apology immediately after the game after video footage of him gesticulating into the crowd, at one stage using a "throat-slitting" gesture.
"When I turned my head, I saw a quarrel with my father," he told Turkish outlet A Spor.
"I didn't know the whole story. I told them that they were wrong, threatened, unworthy of me.
"Character is more important than football. It was an unbecoming gesture. I apologise. I guarantee it won't happen again."
He later offered a fuller apology to Turkish Football, saying:
“I am usually very calm, I lost the plot, a red mist descended on me.
“First of all I would like to apologise to the Turkish people and my teammates, when you wear the national team shirt you have to act responsibly.
“I let my teammates and myself down, we could have gone onto win the game had I not reacted like that.
“But I am human, I am a professional footballer but I am also human. I am very close with my father, he played a huge role in me getting to where I did my career.
“When I saw what happened in the stands I could not hold myself back. All I can do is apologise.”
Quotes sourced from Sportskeeda