The pitch at Dessau's Paul Greifzu stadium was unplayable after it was sprayed by unknown culprits with chemicals, turning the green grass a hard brown.
The DFB has now taken the rare decision of switching the home team for the August 30th tie to Leipzig, in order to play in their stadium at such short notice. Before that, Teutonia had been the host team.
"Because of the imminent date of the match it was not realistic to start a new search for other stadiums, including checking all necessary parameters for staging the Cup game," the DFB said in a statement.
Finding a stadium in which to play the Bundesliga club had been a struggle from the start for Hamburg's Teutonia, with their artificial pitch not eligible for Cup matches.
Hamburg SV and St Pauli - both fellow Hamburg clubs - had refused to provide their stadiums for the game before Dessau, some 400 km (249 miles) away, was chosen.