The DFB said that Zwanziger no longer represented the interests of German football after his "repeated public attacks against his successor as president Wolfgang Niersbach and the current DFB management".
Zwanziger, who held the role of DFB president from 2006 to 2012, criticized his successor's salary in an interview on Saturday.
The DFB in a statement blasted such comments as "intolerable" as they "called into question and discredited the excellent work of the president".
"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," the statement read.
Bundesliga president Reinhardt Rauball added: "These public statements are totally unacceptable, moreover, during a World Cup, in which the players and
the sport should be the focus."
Zwanziger, 69, held various DFB roles before taking over as president in 2006 after Germany hosted the World Cup of which he was vice-president of the organizing committee.
Under his stewardship, Germany reached the final of Euro 2008 and came third at the 2010 World Cup in South Africa.
He resigned in March 2012 and was succeeded by Niersbach. His mandate in Fifa runs until May 2015.