Six fire officials were rushed to hospital after they inhaled excessive smoke during the four-hour operation to control the blaze that broke out at 1:45 AM.
Their condition is said to be stable now, officials said.
Environment Minister Prakash Javadekar, who visited the spot, described the fire mishap as "unfortunate" and ordered a safety audit of all museums under his ministry.
"This is unfortunate...Museum of Natural History is a national heritage. Thousands of exhibits were there and thousands of people visit the museum everyday," he said, adding that officials were ascertaining the extent of the damage and ways to restore it.
As many as 35 fire tenders were pressed into service. It took firefighters more than four hours to douse the blaze after which a cooling operation was launched which lasted for another few hours, a fire official said.
Many exhibits like taxidermied (stuffed) animals and specimens were gutted in the fire.
The cause of the fire is yet to be ascertained, a senior police official said.
