The dead included a woman and a child who had tried to escape by jumping from a fifth-floor window of the 65-room hotel in the shopping district of Karol Bagh.
G.C. Misra, Delhi fire brigade director, said the blaze had been brought under control and that 35 people were rescued by firefighters in an operation lasting several hours.
At least 35 others were rescued from the six-storeyed building, while three jumped off the upper floors of the hotel in Karol Bagh to save their lives.
As per the deputy chief fire officer Sunil Chaudhary, 26 fire tenders were rushed to the spot and also said that 25 personnel were evacuated from the hotel. Some were injured and have been taken to hospital.
Most of the victims were sleeping when the fire broke out, and it was believed to have been caused by a short circuit, according to media reports.
The fire has already raised questions about safety in poorly regulated budget hotels in the country.
"We have ordered for a magisterial inquiry into the case. Many people were still fast asleep at that time", he said, adding that during the dousing process the nine bodies were discovered.
He said they were still investigating what caused the fire.
Frequent raids by civic authorities to enforce building codes, fire safety measures and evacuation procedures have failed to curb violations in a rapidly expanding city of more than 18 million people. "Inside in the rooms, wooden panels were there on the walls", Mr Jain said.
Delhi minister Satyendra Jain told the NDTV news website that the Arpit Palace had built a fifth floor with a kitchen and a terrace, even though the owners only had permission to build four storeys.