Thick smoke engulfed the hospital and firefighters smashed windows to evacuate people down ladders to safety from upper floors. Other patients were rolled out on stretchers.
The fire broke out in the basement and quickly spread through the building by air-conditioning shafts. People said that the fire brigade took an hour to reach the scene.
The vice-president of the AMRI hospital, in a mostly middle class area of Kolkata, told reporters at least 73 people died in the blaze, all but three of them patients. He said 90 patients were safely evacuated.
Angry local residents accused the hospital authorities of reacting too slowly, and pointed out another fire had broken out there three years ago. That time there were no casualties.
Mamata Banerjee, who is both chief minister and health minister in the state, immediately cancelled the operating license for the AMRI hospital, part of a prominent chain of clinics in the city.
The hospital has announced compensation of 500,000 rupees ($10,000) for the families of each victim.