Police chief of Hatay province Cafer Sahin said the explosion was probably "terrorist-linked" in a likely reference to Kurdish fighters, the Anatolia news agency reported on Wednesday.
Those hurt included passers-by and two people sitting on the terrace of a cake shop opposite the bank. The injured were taken to hospital.
The blast blew out windows in nearby buildings.
On Monday, a youth was killed and another injured in an explosion in Antalya harbour, the country's top tourist destination.
Police have refused to say what caused the blast.
Kurdish fighters, who claimed responsibility for the bombing earlier this month of two Istanbul hotels, have warned tourists to stay away from Turkey.
Hatay province has seen clashes between security forces and Kurdish fighters in the past.
Kurdish fighters declared an end to their unilateral truce in June and clashes with security forces have multiplied since in the mainly Kurdish southeast of the country.
On Wednesday, a soldier was killed and another wounded in an ambush near Semdinli, in the south-east of the country, Anatolia said.