The building in the Malviya Nagar neighbourhood in the southern part of New Delhi had a restaurant on the ground floor and a hotel above.
The fire was extinguished on Wednesday but how it started was not immediately clear.
Fire crews rescued 40 people from the building, fire official Abhilash Malik said.
Four bodies were recovered from the site, Jitendra Kumar, a senior administrative official, said.
Images from the scene showed firefighters trying to douse the blaze as thick smoke billowed from the building.
Local residents also joined rescue efforts, helping move people trapped inside and carrying some of the injured to safety.
Some of the victims were foreign nationals who had travelled to India for medical treatment, local media reported.
Many foreign patients travel to New Delhi for medical treatment and often stay in nearby hotels or residential accommodation during their visits.
Prime Minister Narendra Modi expressed his condolences over the deaths, his office said in a post on X.
It also said that the families of those killed would receive 200,000 rupees ($A2900) each in financial assistance.
Fires are common in India, where building laws and safety norms are often flouted by builders and residents.
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