Kuranyi, 28, who was also dropped just before the 2006 World Cup in Germany by then coach Jurgen Klinsmann, was largely expected to return after being banned in October 2008.
He had walked out of the team during a World Cup qualifier against Russia after being dropped from the squad, with Low vowing at the time never to call him up again.
"It was my dream to play in a World Cup ever since I was a kid, like every footballer. Now that dream has gone for the second time," Kuranyi wrote on his personal website.
"The disciplinary affair in October 2008 did not play a role for me," Low said in a statement.
"It would not have posed a problem to give him another chance but in the discussions among the coaches, we came to the conclusion that we had a different idea of the World Cup squad in terms of tactics and players."
"I told Kevin that today and I think he had a great season and is an outstanding professional," Low said.
"I know it was stupid when I walked out of the stadium against Russia at half time," Kuranyi said. "That is why I personally and publicly apologised and this season I gave everything I had."
"Unfortunately it was not enough. But it is the coach's decision and I accept it and respect it."
