"There was a device intended to be detonated inside the stadium," police chief Volker Kluwe told reporters. There were "serious plans to bring something to explode," he said earlier, according Norddeutscher Rundfunk radio.
German media also reported that an ambulance loaded with explosives was found parked nearby, though police have no refuted those claims, saying no explosives were discovered inside the vehicle.
Authorities in Hanover have also evacuated the city's central train station, citing security concerns.
"The game is canceled. The audience is asked to leave the stadium quickly but without a panic," a police spokeswoman said, according to Spiegel.
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According to local authorities, German Chancellor Angela Merkel and a number of German ministers had planned to attend the match, which was called off less than two hours before it was scheduled to begin.
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"Safety is paramount. There is always a fear," Hanover Mayor Stefan Schostok told Sports-Informations-Dienst. "I trust the police have made the right decision, when a threat situation exists, then those steps should be taken."
The Associated Press reports that a bomb threat had been called in earlier on Tuesday, and that policeman Joerg Hoffmeister said that a suspicious object had been found near the HDI-Arena stadium. All roads surrounding the stadium have also been blocked.
A game between Belgium and Spain was also canceled on Monday in Brussels, due to security concerns.
The evacuation comes four days after the deadly attacks on Paris which left 129 people dead and hundreds more injured. Earlier on Tuesday, French authorities also evacuated the Eiffel Tower following a similar bomb scare. That turned out to be a false alarm.