Zondi's resignation comes a month after the resignation of the party's national organiser Albert Mncwango.
Mncwango resigned last month from the position after more than a decade - reportedly at the request of the party's leadership.
His responsibilities included leading the Zululand District and Nongoma constituency.
The IFP had a difficult year in 2011 with its former chairwoman Zanele Magwaza-Msibi leaving the party to form the National Freedom Party (NFP).
In March, Mncwango's wife Sanelisiwe Mncwango defected to the NFP and three days she went back to the party.