Brazil's president, Michel Temer, tweeted that it was "a sad day for all Brazilians."
The museum's collection includes Egyptian mummies, Greco-Roman artifacts, dinosaur fossils and the oldest human fossil from the region, called "Luzia," the Times reported.
The fire began around 7:30 p.m. and there were no injuries, the newspaper reported.
The museum was once the residence for the Portuguese royal family, the BBC reported.
The full extent of the damage is unknown, the BBC said.