The museum contains over 20 million artefacts going back over two centuries.
The fire started at 7.30pm local time and quickly spread to the whole building.
The fire has engulfed each floor of the museum.
No information is currently available about possible casualties.
Brazil’s President, Michel Temer, commented: “It is incalculable for Brazil to lose the collection of the National Museum.
“Two hundred years of work, research and knowledge were lost.
“It is a sad day for all Brazilians”.
The Museo National was founded in 1818 by King John VI of Portugal.
Artefacts held by the museum included the oldest fossil ever found in Brazil, nicknamed ‘Luzia’, and ancient Egyptian and Roman items.
More to follow…