Dačić was born on 1 January 1966 in Prizren, which at the time was part of the Socialist Republic of Serbia within Yugoslavia. Dačić was born to a Serbian family and was brought up in Žitorađa. His father, Desimir, was a police officer, and his mother, Jelisaveta ("Jela"), was a housewife. His parents were both born in villages under the Jastrebac. When Ivica was six months old, the family moved to Žitorađa. He has a sister, Emica. At the age of 5, he was featured in the newspapers in the article "Enciklopedija u kratkim pantalonama" (Encyclopaedia in shorts) as he had learnt to read and write himself, knew the names of many mountains, rivers and capitals, nearly all notable football players and results of matches.