The explosion -- which took place near a building where prosecutors are housed -- was caused by a car bomb in the district of Viransehir, official news agency Anadolu cited governor Gungor Azim Tuna as saying.
He said the dead child was the son of a court worker, adding that the wounded were taken to hospital but were not believed to have any serious injuries.
Tuna said the blast was a "terror attack" caused by a parked vehicle that was loaded with explosives and detonated using a remote control.
Justice Minister Bekir Bozdag said on Twitter that no terrorist organisation or attack would weaken Turkey's fight against terror.
"Our determined and effective fight against terror will continue," he said.
No group immediately claimed the attack, and Bozdag did not say which organisation the government suspected.
Turkey was hit by a series of attacks in 2016 blamed on Kurdish militants and Islamic State (IS) jihadists, killing hundreds of people.
This year also had a bloody start, with a New Year's attack on an elite Istanbul nightclub which left 39 people dead, most of them foreigners. The attack was claimed by IS.
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