The blaze started at 8:40 a.m. on the third floor and spread to the fourth floor, firefighters said. It was extinguished seven hours later.
At the time of the fire, the museum was closed for renovations, and no visitors were inside.
Two construction workers were rescued, and four others were evacuated safely.
One firefighter was injured by falling steel reinforcement bars and was taken to a hospital.
The state-run museum opened in 2014 to preserve and promote Hangeul, the Korean writing system.
It has been undergoing renovations since October to expand its educational facilities and was scheduled to reopen in late 2025.
The museum's collection, including valuable items such as King Jeongjo's Hangeul letters from the Joseon Dynasty and Korea's first anthology Cheongguyeongon, had been moved to secure storage before renovations began, museum officials said.
The artifacts were transferred to the nearby National Museum of Korea later on Saturday as a precaution.
Fire authorities deployed about 140 firefighters and 39 pieces of equipment. They struggled to contain the blaze due to construction materials blocking access.
Authorities are investigating whether sparks from steel cutting during construction triggered the blaze.
Culture Minister Yu In-chon visited the site and called for full cooperation with the National Fire Agency to contain the fire.
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