The attackers struck near a former police station used by Saraya al-Salam, a Shiite paramilitary force led by powerful Shiite cleric Moqtada al-Sadr, the official said on condition of anonymity.
Twelve people were also wounded in the two explosions, about 15 minutes apart.
The first attacker blew up an explosives-rigged car, followed by the second, who used an explosive belt, the official added.
The attack struck Atlas Street, a key shopping area in the heart of the city of a million residents.
Sadr's force, formerly known as the Mahdi Army, is part of the Hashed al-Shaabi paramilitary alliance that has battled both the Islamic State group and Kurdish forces.
Iraqi security forces backed by the Hashed in mid-October seized oil-rich Kirkuk province from Kurdish peshmerga forces in the wake of a Kurdish independence vote held in defiance of Baghdad.
Kurdish media have since accused the Hashed, an alliance composed mainly of Shiite militias, of carrying out a campaign of retribution against Kurdish civilians.
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