The castle normally serves as the presidential residence, but BNS said Latvian president Andris Berzins is staying elsewhere as the building is being renovated.
BNS said the fire started late Thursday and raced through the attic and roof.
Video from Latvian TV showed flames shooting up from the roof, sending a thick plume of smoke into the night sky.
The extent of the damage is not immediately clear, including whether the fire damaged the museum and its artefacts.
There are no reports of injuries.
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