Evacuation of the Hannover Stadium, which was hosting the match, began less than two hours before kick-off.
The city's president of police Volker Kluwe told the BBC "there were plans for some kind of explosion".
German Chancellor Angela Merkel was set to attend the match at the 49,000-capacity HDI Arena.
Belgium's friendly with Spain on Tuesday in Brussels was called off on Monday because of security fears in the wake of last week's attacks in Paris.
England's match against France at Wembley on Tuesday night is going ahead, with tributes to be paid to the 129 people killed in Paris on Friday.]