It follows reports that a secret €6.7m (£4.9m) fund was set up to secure votes for Germany to host the 2006 World Cup.
The DFB denied the claims last month, reported in Der Spiegel news weekly.
In a statement, the prosecutor`s office said it had opened a probe into claims of serious tax evasion linked to the awarding of the World Cup in 2006.
It said it was investigating the alleged transfer of €6.7m from "the organising committee for the DFB to the Fifa football association".
Mr Niersbach has denied the allegations, claiming instead that the sum was used to secure larger Fifa funding.
But, speaking to Der Spiegel, Mr Zwanziger accused his successor of lying, saying it was "clear that a slush fund existed".
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