Džafer Kulenović was born to a Bosniak family in the village Kulen Vakuf near Bihać, Bosnia and Herzegovina, Austria-Hungary. He was the son of Muhamed-beg Kulenović and his wife Meleća. He had an older brother, Osman (1889–1947), a politician and lawyer. Kulenović attended gymnasium in Sarajevo and Tuzla, and he was expelled from school in 1905 just two months before graduation due to a clash with Serbian students; because of that he transferred to school in Mostar and graduated there in 1909. In the same year, he entered the University of Vienna, but because of health issues he went to Faculty of Law, University of Zagreb from which he graduated. Kulenović was active in Vienna's Party of Rights' youth organization of pro-Croat Muslims, Svijest (The Awareness), and was elected its president.
In 1919, after the Kingdom of Yugoslavia was established, Kulenović joined the Yugoslav Muslim Organization, a political party of Bosnian Muslims. For every election held in Yugoslavia, he was elected to the National Assembly as a representative of the Brčko municipality. When the Vidovdan Constitution was voted on, his party ordered its members in the National Assembly to support the new constitution; however, Kulenović boycotted the voting as he was against the Constitution and thus didn't violate his party's orders. In 1921, he protested to the Assembly the massacre of 200 Muslims carried out by Serbs in northern Montenegro. When his party divided into the Centralist (pro-Serb) and the pro-Autonomy list, Kulenović supported the pro-Autonomy.
In the 1923 election, the Autonomists defeated the pro-Serbian faction. Kulenović was also among those who made the Sarajevan Punctations, in which the YMO condemned the Serbian nationalist policy over Bosnia and Herzegovina and demanded Bosnian autonomy. After Mehmed Spaho, the President of the YMO, died, Kulenović was elected as the organization's new president on 29 June 1939. Uzeir Hadžihasanović who was influential amongst the Muslims, helped him win this post. At this time, the YMO was in a coalition called the Yugoslav Radical Union (YRU); the coalition was led by Milan Stojadinović. The YMO's membership in the YRU threatened YMO's existence, and Kulenović tried to save the party. His actions led to the division in the YRU.
During the crisis of the YRU, Kulenović stated to the press: Gentlemen, I am a Croat and a Croatian nationalist... And not only that I am a Croat and a Croatian nationalist, but the Bosnian Muslims are, as a whole, Croats and part of the Croatian nation.
During the tenures of prime ministers Dragiša Cvetković and Dušan Simović, Kulenović was a minister without portfolio and Minister of Forestry and Mining. In 1939 Kulenović opposed the partition of Bosnia and Herzegovina when the Banovina of Croatia was created, and he also opposed the idea of Serbian nationalist ministers and politicians that the parts of Bosnia and Herzegovina, which were not included in the Croatian Banovina, should be included in Serbian lands. During the German Invasion of Yugoslavia in April 1941, Kulenović didn't leave the country as most ministers did; he secretly left Belgrade and went to Užice, from where he went to Sarajevo and later to Brčko, where his family lived.
He became the vice-president of the Independent State of Croatia (NDH) on 7 November 1941 and held the position until the end of the war. He had succeeded his older brother Osman Kulenović in this position. At the end of the war he fled to Austria. He was apprehended by British forces and sent to their detention centre at Spittal an der Drau on 17 May. He arrived one day after a group of NDH government officials had been sent back to Yugoslavia.
Kulenović later immigrated to Syria. He lived there until his death on 3 October 1956 in Damascus. While in Syria, the expatriate Croat community in Argentina published a collection of his journalistic writings. In 1950, the Bosnian Muslim Community in Chicago published a speech he wrote for the Muslim Congress following World War II in Lahore, Pakistan.