"Eighteen of our citizens have been taken to hospital, among them a 10-year-old child who lost their life," the office said yesterday, adding that one of the injured was in a serious condition.
The explosion -- which took place near a building where prosecutors are housed -- struck the district of Viransehir, the office added.
Earlier the official Anadolu news agency had cited governor Gungor Azim Tuna as saying the dead child was a three-year-old boy.
The lodgings were badly damaged, the governor added, while Dogan news agency said other buildings and several cars in the area were also damaged.
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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. The country was also shaken by a failed military coup last July.
Last month the Kurdistan Freedom Falcons (TAK), a splinter group of the outlawed Kurdistan Workers' Party (PKK), claimed responsibility for an attack that left two dead in the Aegean city of Izmir.
The PKK has been waging an insurgency against the Turkish state since 1984 during which over 40,000 people have been killed. It is proscribed as a terror organisation by Ankara, the United States and the European Union.