The blaze started on the sixth floor of the National Museum of Natural History early on Tuesday and rapidly spread to all seven floors, reports said.
More than 30 fire engines tackled the blaze. Six firemen were injured.
It is not yet clear what caused the fire at the 38-year-old museum in the heart of the city.
Environment Minister Prakash Javadekar said officials had yet to determine the full extent of the damage but old collections had been destroyed.
"This is a real loss. This loss cannot be counted in rupees. Some very old species of flora and fauna were there," Mr Javadekar was quoted by the AFP news agency as saying.
A fire officer told the NDTV news channel that the building's "fire safety mechanisms were not working".
"That is why it took us so long to douse the fire. The cooling off process is still on," he said.
The museum housed galleries with "herpetological specimens, preserved butterflies, and mounted specimens" of animals, according to its website.
The museum contained preserved specimens of butterflies, frogs, snakes, lizards as well as mounted specimens of tigers and leopards.
It was also popular with school children and screened films on wildlife and ecology.
The museum had been criticised for "being badly designed and poorly maintained", and there were plans to move it to a new building at another location.
A fire has destroyed a museum in the Indian capital, Delhi, ruining rare specimens of flora and fauna, India's environment minister has said.