Police said they believed the bomber, Suelee Jehni, had been killed by the blast on Friday at around 9am (0200 GMT) near the bank's automated teller machine.
Three soldiers were among the six men and two women wounded. One soldier was in a critical condition.
The bomb shattered windows up to the third floor of the Siam Commercial Bank branch in Sungai Kolok, a tourist town best known for a strip of bars and brothels which lure tourists from neighbouring Malaysia.
"We suspect the dead man may have some connection with members of these militant groups," Lieutenant-General Manoj Kraiwong, commander of the southern police region, told a Bangkok radio station.
"It seems the bomber targeted the three special army force personnel who stopped to withdraw money from the ATM," he said.
Third bomb attack
It was the third serious bombing the town has suffered since March 2004, increasing pressure on the government as it heads into a general election next February.
In October, two people, including a Malaysian tourist, were killed and 20 wounded by bombs that exploded at two tourist bars in Sungai Kolok.
In March, a bomb hidden in a motorcycle exploded at a karaoke bar on the same tourist strip, wounding 28.
Altogether about 500 people have been killed this year in the three provinces of Pattani, Narathiwat and Yala, which once were part of a sultanate annexed by Thailand a century ago.