Some people were on fire as they ran out of the building, the Yonhap news agency quoted a witness as saying.
An official at the National Emergency Management Agency said authorities were struggling to identify the dead due to their burns, but a police official said at least two Japanese were confirmed killed.
Nine Japanese tourists and their South Korean guide were inside the facility in the southeastern port city of Busan when the fire broke out on the second floor of a five-story building, police official Han Jong-seok said. He said it was not known how many other people were in the building at the time.
A Japanese man was in life-threatening condition with severe burns at Dong-a University Medical Center in Busan, said Kim Won-ha, an emergency room nurse.
Four people - two Japanese and two South Koreans - were being treated for burns over 50 percent to 90 percent of their bodies at Hana hospital in Busan, which specializes in burn treatment, the hospital said.
The Japanese Embassy in Seoul said officials had yet to confirm the exact number of Japanese victims.
The emergency official, who spoke on condition of anonymity citing policy, said the fire raged for about 40 minutes before being put out. Police and fire officials were trying to determine its cause.
