On Wednesday afternoon, the flames quickly spread from the building on August 23 Street in Hue Town that displays artifacts from the war against French colonialism, sending columns of smoke up dozens of meters.
Firefighters were dispatched to the scene. After an hour, the fire was put under control.
Part of the building's roof had collapsed while many items displayed inside were burned.
Police are investigating the cause of the fire.
The ancient building was part of Hue Imperial Academy, or Quoc Tu Giam, constructed in 1908 by King Duy Tan, the 11th king of Vietnam's last ruling family Nguyen (1802-1945).
After the Vietnam War, the academy was turned into Thua Thien-Hue History Museum.
In 1993, Hue Imperial Academy and other royal relics of Nguyen Dynasty were inscribed on the UNESCO World Heritage List.