Kiš, was born in Subotica, Danube Banovina, Kingdom of Yugoslavia (now Serbia). Kiš was the son of Eduard Kiš (Hungarian: Kis Ede), a Hungarian-speaking Jewish railway inspector and Milica (née Dragićević), a Montenegrin Christian from Cetinje. His father was born in Austria-Hungary with the surname Kohn, but changed it to Kiš as part of Magyarization, a widely implemented practice at the time. Kiš's parents met in 1930 in Subotica and married the following year. Milica gave birth to a daughter, Danica, in Zagreb in 1932 before the family relocated to Subotica.
Kiš's father was an unsteady and often absent figure in Danilo's childhood. Eduard Kiš spent time in a psychiatric hospital in Belgrade in 1934 and again in 1939. Kiš visited his father in the hospital during one of his later stays. This visit, in which, Kiš recalled his father asking his mother for a pair of scissors with which to commit suicide, made a strong impression on young Danilo. For many years, Kiš believed that his father's psychological troubles stemmed from alcoholism. Only in the 1970s did Kiš learn that his father had suffered from anxiety neurosis. Between stays in the hospital, Eduard Kiš edited the 1938 edition of the Yugoslav National and International Travel Guide. Young Danilo saw his father as a traveler and a writer. Eduard Scham, the eccentric father of the protagonist of Early Sorrows, Garden, Ashes, and Hourglass is largely based on Kiš's own father.