By Agence France-Presse
Rio de Janeiro
The cause of the fire, which broke out around 2230 GMT, was not yet known, according to local media.
Television footage showed the building engulfed by a raging blaze that firefighters had not brought under control.
The museum was founded in 1818 by King Joao VI and is among Brazil's most important, with valuable national treasures inside.
"This is a tragic day for Brazil," President Michel Temer said in a statement. "Two hundred years of work and research and knowledge are lost."
"This is a cultural tragedy," the director of the National History Museum said on Globo TV.