The victim's mother had hired a maid servant and used to drop her daughter at her house before going for work in a garment shop. On July 25, the girl was raped by the man when his mother was away, a senior police official said.
The incident came to light on July 29 and the case was filed today, Additional Commissioner of Police (Law and Order) Alok Kumar said.
Police have registered a case of rape and were investigating further.
The incident comes close on the heels of the alleged gang rape of a six-year old girl at Vibgyor High School on July 2, a shocking incident that caused public outrage and led to severe protests over growing crime against women and children.
Two gymnastics instructors were arrested on Monday in connection with the school incident while the police ruled out the "direct" involvement of the skating instructor Mustafa who was earlier arrested as main accused.