Žigić was born in Bačka Topola, in what was then SFR Yugoslavia, the son of Jovan, a former footballer, and his wife Milica, who had been a basketball player. He completed his secondary education at the mechanical engineering school in Bačka Topola. His brother Branko, 15 months his junior, also became a footballer, as a central defender with clubs including Cement Beočin and Serbian First League club Proleter Novi Sad. During the Yugoslav Wars in 1999, Žigić's hometown was beneath the flight-path of NATO bombers heading for Belgrade; for much of that part of the conflict, the family home was without electricity or running water.