The match was due to have been held four days after deadly attacks in Paris on Friday, when suicide bombers targeted the football stadium where Germany were playing France.
"We had received specific indications that an attack with explosives was planned," Hanover Police President Volker Kluwe told NDR state broadcaster.
"We took them seriously and that is why we took the measures."
Police vans with loudspeakers ordered fans to leave the Hanover stadium and heavily armed officers positioned themselves outside the arena.
Police also evacuated Hanover's TUI multi-purpose arena where a concert was about to start.
Interior Minister Thomas de Maiziere said the threat was credible and cancelling the game was the right thing to do, but did not provide any details.
"I understand the question but I will not answer it," he told a hastily convened news conference when asked what had forced the decision.
He said divulging details could undermine security at other events.
"We will have such cases in the future, maybe not Hanover but somewhere else," he said.
Lower Saxony interior minister Boris Pistorius said no explosives had been found and no arrests had been made.
After the attacks in Paris on Friday security measures in Hanover had been tight.
In a show of solidarity, Merkel was set to attend with Vice Chancellor Sigmar Gabriel and several government ministers.