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The pilot of a third plane who witnessed the accident said parachutes had been ejected from both aircraft. One of the pilots was later rescued from the top of a tree but the other was found dead on the ground.
"This is a sad day for our air force," Defence Minister Ursula Von Der Leyen told reporters near the crash site in the eastern state of Mecklenburg-Vorpommern.
"We lost a soldier in a flight accident. Our thoughts are with his family and his comrades."
The jets collided about 20 minutes after they took off, she said. An armed forces spokesman said it was too early to say anything about the circumstances of the crash, and recovery teams were searching for the black box flight recorders.
The battalion based at Laage air force base, near Rostock, where the aircraft took off, trains all pilots flying Germany's 140 Eurofighters.
They were the first two of the jets that Germany has lost since it started flying them in 2004.
Ostseewelle radio, which first reported the crash, posted a video sent in by a listener which it said showed two plumes of smoke rising from separate crash sites some distance apart.
It described a field of debris around the area of the crash, which it said had ignited a small forest fire.
About 400 Eurofighters - made by a consortium of Airbus , BAE Systems and Leonardo - are in service around the world.