Ozil will miss the World Cup winners' upcoming Euro 2016 qualifiers against Poland and Ireland as well as matches against Gibraltar and Spain later this year.
"The 25-year-old complained about pain in his left knee when he arrived in Frankfurt (to join the Germany team) on Tuesday," the DFB said in a statement.
"The scan today... revealed a partial tear of his exterior ligament in his left knee. He will be out an expected 10-12 weeks,” the DFB added.
Ozil, who played the full 90 minutes in Arsenal's 2-0 Premier League defeat to Chelsea on Sunday, is the latest big name absence from coach Joachim Loew's squad along with Bastian Schweinsteiger, Sami Khedira, Mario Gomez and Marco Reus.
Chelsea's Andre Schuerrle also missed team training for the second day in a row, undergoing an individual session but officials were hopeful he could be fit in time for Saturday.
"It is going to be a tough October," Germany team manager Oliver Bierhoff told reporters.

"It is a special situation as world champion. Expectations are high and the opponents' motivation to beat Germany is even greater now. We want two wins to have a successful October," he said.
There was some good news for the Germans with attacking midfielder Julian Draxler expected to join up with the team later on Wednesday after overcoming flu.
The Germans, who won their opening Group D game against Scotland last month, face Poland in Warsaw on Saturday and host Ireland in Gelsenkirchen next week.

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