Many of the dead people were patients who were trapped after the flames spread through the AMRI hospital in the southern part of Calcutta.
Fire engines fought the blaze for five hours before bringing it under control.
West Bengal Chief Minister Mamata Banerjee said the license of the hospital had been cancelled.
Mamata Banerjee said fire was an “unforgivable crime” and that those responsible would be given the harshest punishment.
Officials say the death toll is likely to rise as rescue workers are trying to reach the upper floors of the six-storey hospital in Dhakuria.
A Upadhay, a senior vice-president of the AMRI hospital company, told Associated Press there were 160 patients in the 190-bed hospital.
West Bengal Urban Development Minister Firhad Hakim said many of the patients who died had suffocated on fumes.
A number were rescued. “We have taken 50 patients to an adjacent hospital. The situation is grim at the moment,” fire brigade chief Gopal Bhattacharya told Agence France-Presse news agency.
Bodies of patients wrapped in white sheets have been brought out by rescue workers, BBC reported.
Local people climbed into the hospital compound to rescue patients before fire engines arrived, our correspondent says.
The narrow surrounding streets made it difficult for the rescue service to arrive quickly.
The fire spread swiftly from the basement to the upper floors of the private hospital.
Television pictures showed patients being carried out on stretchers, with distraught relatives of trapped patients crowded outside the building.
One rescued patient said: “The attendants woke me up and dragged me down the stairs. I saw 10-15 patients at the top of the stairs trying to get down.”
Ananya Das, 35, who underwent surgery at the hospital on Thursday, said she was recovering when the fire broke out.
“I managed to walk towards an exit and then climb out of a window. I saw a lot of bodies,” she said.
More than 40 people died in a huge fire in a historic building in Calcutta in March last year.
Fires in high-rise buildings are fairly common in the city. There have been at least 10 major incidents since 2008.
Electrical short circuits have been responsible for most of these fires.
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