The explosion struck the district of Viransehir on Friday night, killing a 10-year-old and a neighbourhood watch guard.
The office said 26 people were detained including the suspected owner of the car used in the blast, which Dogan news agency said was caused by a tonne of explosives.
Some 17 people were also injured in the attack on a housing complex where courthouse workers and security personnel live.
Sanliurfa governor Gungor Azim Tuna told the official news agency Anadolu that the outlawed Kurdistan Workers' Party (PKK) was to blame.
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The PKK is proscribed by Ankara, the United States and the European Union as a terror group.
The group has been waging an insurgency against the Turkish state since 1984 during which over 40,000 people have been killed.
Last year saw a series of attacks in Turkey blamed on Kurdish militants and Islamic State (IS) extremists while 2017 began with a bloody start.
During New Year celebrations a suspected IS jihadist killed 39 people, most of whom were foreigners, in an armed attack on a popular Istanbul nightclub.
The latest attack came after President Recep Tayyip Erdogan kicked off his campaign for a "yes" vote at the April 16 referendum on expanding his powers in the province of Kahramanmaras, close to Sanliurfa.