Ozil has had a tough time in Arsenal colours lately, missing a crucial penalty against Bayern Munich in the UEFA Champions League last month.
He started his first season in the Premier League superbly but he has been struggling for form in recent weeks.
The midfielder set up the only goal of the game for Mario Gotze in Stuttgart, but when he was substituted a minute from full-time he was jeered and whistled by the home supporters.
Ozil's Germany team-mates leapt to his defence, with defender Jerome Boateng saying: "They have some nerve. You can't shine all the time."
Team manager Oliver Bierhoff added: "I don't understand the whistling. I find it a shame that a player such as Mesut is picked out. I would hope for different support for a game like that."
Coach Joachim Loew admitted the whole team were poor.
"We weren't capable of dominating the game. It is always good when one can see that Germany is not the only country to have good players," he said.