The accused, a 40-year-old security guard who worked in the building the child lived in, has been arrested.
Police found the girl unconscious and rushed her to hospital where she is undergoing surgery.
The incident occurred on Sunday, which was the sixth anniversary of the brutal gang rape of a student on a Delhi bus.
Delhi Women's Commissioner Swati Maliwal said the incident "let down" the bus rape victim, whose attack saw country-wide protests and a tightening of rape laws.
There is still no clarity on the condition of the girl or whether she will survive the attack, which local media have described as "brutal".
Locals in the area found the accused and attacked him after the incident came to light, the Times of India newspaper said. It also quoted police as saying that the accused was treated for injuries before they arrested him.
The girl's parents, who are daily wage labourers, were away when the incident occurred. The accused allegedly lured the girl with sweets and picked her up from outside her house.
Police have registered a case for rape under the Protection of Children from Sexual Offences (POSCO) Act, which could see the death penalty handed out to the accused.
The incident, which has prompted a fresh wave of anger and outrage in India, comes after a series of high-profile cases against children this year. In April, the brutal gang-rape and murder of an eight-year-old in Indian-administered Kashmir dominated headlines. In June, hundreds took to the streets in the central state of Madhya Pradesh over the rape of a seven-year-old girl.