The blast, near a major hospital in the predominantly Shi'ite Muslim city, was caused by a motorbike rigged with explosives, the military said in a statement, citing preliminary information.
There was no immediate claim of responsibility.
"The blast carries fingerprints of Daesh (Islamic State)," Basra Governor Asaad al-Edani told reporters.
Bomb attacks in the Basra area been rare - the last major one was in 2017, and claimed by Islamic State. The authorities have kept a tight grip on the area where the bulk of the OPEC member's oil is produced and exported.
Policemen were collecting body parts from a minibus that was badly damaged by the blast, a Reuters witness said. The street was covered with broken glass and blood. The governor announced three days of mourning.
"Today and after this terrorist act, the people of Basra must definitely be cautious and careful. Basra became unsafe today," said Mohammed Ibrahim, a car mechanic whose workshop was near the blast site.
Police and hospital sources earlier told Reuters that 20 people had been wounded, in addition to the four fatalities.
Helped by a US-led coalition and Iran-backed forces, Iraq declared victory over Islamic State in December 2017, after driving it from swathes of territory where it had declared a self-styled Islamic Caliphate.
But the militant group continues to carry out sporadic attacks, particularly in the north, where Islamic State briefly seized a village on Sunday before being driven out.