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Anuj Sharma, the fire services director of West Bengal state, said the fatalities included a child and that thick smoke had engulfed the hotel.
He added that some of the victims were found in bathrooms.
Preliminary information suggested that an air conditioner may have exploded, triggering the fire, although authorities were continuing to investigate the incident.
Nine people, including six men, two women and a child, were rescued from the hotel and taken to hospital.
Santosh Pathak, a member of West Bengal's ruling party, said some of the victims appeared to be Bangladeshi nationals who had travelled to Kolkata for medical treatment, and that authorities were working to confirm their nationalities.
A total of 60 guests were staying at the budget hotel when the fire broke out.
Building fires occur frequently in India, where inadequate firefighting equipment and non-compliance with safety regulations have contributed to deadly incidents.