The 26-year-old was missing after the World Cup qualifier in Dortmund, after being omitted by coach Joachim Low from the game's 18-man squad.
Low vowed not to select Kuranyi for the national Mannschaft in the future, but the Schalke striker issued a public apology on Monday.
"It was wrong to leave so early and I have apologized for that," Kuranyi said.
"I always felt happy with the national team. I have never had a personal problem with a coach - not at club level nor at international level.
"I have always tried to understand people and that is the way I am naturally. But I have left them in the lurch."
Dortmund Stands
It was claimed that Kuranyi's act came in response to his omission, but the Brazilian-born forward had another explanation for his early exit.
As a Schalke player, sitting in the stand in Dortmund is hard enough," he added.
"Nobody knows what is going on inside my body, in my mind and how bad it all is.
"The Germany coach has accepted my apology and he knows full well why I reacted like I did and understands me. It all just got too much for me."