Mr Erdogan said the so-called Islamic State (IS) was behind the attack, which targeted a Kurdish wedding party. Gaziantep, near the Syrian border, is known to have several IS cells.
The bomb wounded 69 people, Mr Erdogan added, 17 of them seriously.
The bomber targeted the wedding guests as they danced in the street.
The BBC's Seref Isler, who is from Gaziantep, says the city of 1.5 million was already on edge because of events in Syria, where IS has been battling Syrian Kurdish forces.
A suicide bomber believed to have links to IS killed two policemen in Gaziantep in May.
IS is known to have operatives in Gaziantep.
Turkey has been hit by a series of bombs both by IS and Kurdish militants in the past year. The last IS attack, on Istanbul airport in June, killed more than 40 people.
The jihadists have recently lost ground in northern Syria, including a former stronghold, Manbij. Syrian rebel soldiers are preparing to advance further into the IS-held province of Jarablus.
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