In October, Beckenbauer, 70, said he made a "mistake" in the bidding process for which he took "responsibility".
Germany beat South Africa 12-11 in the vote, which took place in July 2000.
German news weekly Der Spiegel reported last year that an alleged slush fund of 6.7 million euros (£4.8m) was used to buy votes for Germany. The allegation was denied by the DFB.
Beckenbauer, Zwanziger, Schmidt and Hans are to be investigated for "possible undue payments and contracts to gain an advantage in the 2006 World Cup host selection", while Niersbach and Sandrock will be investigated for a "possible failure to report a breach of the Fifa code of ethics".
Beckenbauer was the head of the World Cup organising committee, which reports allege made a payment to Fifa in return for a financial grant.
He captained West Germany to victory as hosts at the 1974 World Cup and was coach when they next lifted the trophy, in Italy 16 years later.
The former defender went on to manage French side Marseille and German giants Bayern Munich, where he is now honorary president.
More about:
