"I cannot accept a reaction such as that shown by Kevin, and therefore I will no longer select him in future for the national side," Low said in a statement on the German Football Federation (DFB) website.
Kuranyi, who was left out of the 18-man squad that beat Russia 2-1 on Saturday, has reportedly left the team's camp without permission after the win in Dortmund.
SID news agency reported that a couple of the 26-year-old's friends picked up his possessions from the team's hotel in Dusseldorf.
German team officials searched for Kuranyi after the game at Signal Iduna, while manager Oliver Bierhoff failed to reach him on mobile phone.
Kuranyi, who has 52 caps for Germany, has hardly played regularly under Low, who usually counts on Miroslav Klose and Lukas Podolski upfront.