Hanover city police chief Volker Kluwe said there had been "serious plans to cause an explosion" in the 49,000-capacity stadium, and that authorities had acted on "a concrete threat scenario".
"We received a serious indication that a bomb attack was planned inside the stadium tonight," he told public broadcaster ARD.
Thousands of fans were evacuated, without signs of panic, from Hanover's HDI Arena, as hundreds of police, some on horseback, secured the area.
The German team was playing France in Paris last Friday when players and fans were shaken by the blasts of three jihadist suicide bombers outside the Stade de France that echoed through the venue.
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Head coach Joachim Loew had called Tuesday's planned match "a clear message and symbol of freedom and a demonstration of compassion, as well as sorrow, for our French friends -- not only in France, but throughout the world".
Before the match, players had been practising the French anthem "La Marseillaise", which they had been set to sing in a sign of solidarity with the shaken neighbouring nation.
"We didn't even get into the stadium before we heard it was called off," he said, walking away with his girlfriend Judith.
"There was no information about why the game was called off, security has to come first I guess. But it's going to be a pretty sad journey back to Dortmund for us now for nothing."
The victims of the Paris attacks -- which claimed at least 129 lives with more than 350 injured -- had been set to be honoured by candlelight in what had been described as "a friendly in the true sense of the word".
The German team are still coming to terms with what they experienced last Friday during their international against France.
"There was a lot of fear and anxiety in the dressing room that night," said Loew. "We were afraid.