A group of several attackers planned to set off multiple explosives in Hanover soccer stadium at Tuesday night's friendly match between Germany and the Netherlands, which was called off, daily Bild reported on Thursday.
The packet was sent from Athens by air mail two days ago disguised as books and the explosive device hidden inside was "very similar" to the parcel bomb, which exploded on Tuesday at the Swiss embassy in Athens, German Interior Minister Thomas de Maiziere said.
The cabinet ministers concerned are on their way to Berlin.
Germany's main anti-immigrant party triggered outrage on Sunday when its vice-chairman said people would not want German black soccer star Jerome Boateng as their neighbour.
Germans basked in World Cup glory again when the national team were honoured before attending the premiere of the official movie about their victory in Brazil in July.
As thousands of asylum-seekers continue to stream into Europe, Germany has called upon its European Union partners to agree on a common policy.
German Chancellor Angela Merkel said the attack was linked to terror.
French air investigators are examining one of the black boxes of the doomed Germanwings plane to find out why the aircraft crashed into a mountain in the French Alps, killing the 150 people on board.
Hundreds of migrants, who continue to arrive in Europe as they flee the scenes of chaos and brutality of the Islamic State in the Middle East, have created sharp divisions among European Union member states which are increasingly finding it tough to control the massive influx.
As German makes provisions to accept 800,000 refugees this year, the nation is split vertically on the crisis with refugee shelters attacked with Molotov cocktails and swastika signs painted outside many refugee homes.