The dead are thought to include three Sri Lankan nationals, local media reports say.
Twenty five others were injured in the fire, which is reported to have broken out on Saturday evening.
Witnesses reported hearing a loud bang before smoke filled the bar. The cause of the fire is under investigation by police.
"Firefighters believe the fire might have been caused by a short circuit," a police spokesman told Agence France Presse.
Customers at the bar were unable to find exits due to smoke, police told the Yonhap news agency.
All of the victims died from inhaling toxic gases, police say.
One of the injured is reported to be in a serious condition, but none of the others is believed to have sustained life-threatening injuries.
About 20 fire trucks and 100 firefighters battled the fire and extinguished it around 22:00 local time on Saturday (13:00 GMT), Yonhap reports