Zwanziger has come under fire of late after publicly criticising the German governing body and, in particular, his successor Wolfgang Niersbach.
A DFB statement on Saturday criticised Zwanziger's behaviour and requested he leave his role at FIFA.
"Since he does not adequately represent the ... interests of German football, the DFB calls on Dr Theo Zwanziger to resign from his position on the Executive Committee of FIFA," it read.
League president Dr Reinhard Rauball added: "These public statements are totally unacceptable, moreover, during a World Cup, in which the players and the sport should be the focus."
And those comments were echoed by secretary general Helmut Sandrock, who said: "We again have under Wolfgang Niersbach a climate of trust that had previously been lost.
"These public allusions are not only wrong, but also bad style."