The blaze reportedly erupted in the seven-storey building after an explosion was heard on Thursday morning.
The fire is being investigated as arson after a 50-year-old man was identified through security camera footage as the suspect. The man, who has not been named so far, died at the site.
The officials have not immediately released information about the potential motive behind the arson.
Jeong Hyeon-wook, an official from Daegu Metropolitan Police, said the footage showed the suspect leaving his house with what seemed to be a container in both hands. This may have been used to set the fire, he said.
Mr Jeong added that all the dead victims were found in the same room.
The fire erupted around 10.55am local time in a building in Beomeo-dong next to Daegu District Court, an affluent business district that is 130km from the capital Seoul.
Authorities said they received reports of a loud explosion from the law firm’s offices and subsequently, witnesses saw thick black smoke emanating from the building, Yonhap News Agency reported.
At least 41 people were being treated, most of them from smoke inhalations, while 26 were receiving treatment for burn injuries in hospitals, said Park Seok-jin, chief of Daegu’s Suseong district fire department.
Nearly 60 fire engines and about 150 firefighters rushed to the scene and controlled the fire in about 20 minutes.
Mr Park said firefighters used windows to access the insides of the office and carry out rescue and fire control efforts.
While the identity of the suspect has not been revealed, local news outlets reported that the police were investigating whether the fire was caused by an enraged client over a case.
Daegu is a city in South Korea with a history of one of the worst arson attacks in 2003, when 192 people died after a 56-year-old man set fire on a subway train. The fire spread to two trains within minutes and has been recorded as the deadliest deliberate loss to multiple lives in a single incident.