A total of seven fire tenders were rushed to the spot, they said.
Amjad, his sisters Zarina (one-and-a-half years old), Alifa (eight years) and their father Mohammed Jahoor (52) were pulled out from the debris.
According to police, Amzad was declared brought dead at the Lady Hardinge Hospital, while his three injured family members are undergoing treatment.
The Paharganj police station had received an information about a building collapse, they said.
The four-storey old building in Main Bazar, Paharganj is in a dilapidated state. Only one family was residing in the building on the first floor, while it houses several shops on the ground floor, Deputy Commissioner of Police (central) Shweta Chauhan said.
On Thursday evening, the roof of the second floor collapsed on the first floor in which the family was residing, and that roof also fell down under its impact. The resident of the first floor, Mohammed Jahoor, and his three children Amjad, Arif and Zarina got trapped under the debris, the DCP said.
Local police are present at the spot and there is no gathering. Legal action is being taken, police added.
A senior fire official said a search is on for other people suspected to be trapped under the debris.