The blaze erupted in the early hours of Wednesday at a hotel in central Kolkata close to the West Bengal Fire Department headquarters, the Press Trust of India news agency reported.
Five fire engines were deployed to bring the blaze under control, while police and disaster management teams carried out rescue operations, the report said.
The injured were taken to a nearby hospital for treatment.
Firefighters struggled to reach people trapped on the upper floors as thick smoke engulfed the building, a police officer told the news agency.
The fire was brought under control, the officer said.
Authorities said their immediate focus was on rescuing anyone still trapped inside and investigating the cause of the fire, which was not immediately known.
Nine people had been confirmed dead but the toll could rise, police told PTI.
Deadly fires, often linked to electrical faults or gas cylinder explosions, are common in India where investigators have frequently pointed to safety lapses and inadequate enforcement of fire regulations as contributing to recurring loss of life.
On Monday, a blaze at a hotel in West Bengal's temple town of Tarapith left at least seven people dead and several others critically injured.
In December, at least 25 people were killed after a fire ripped through a popular nightclub in western Goa state.
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