The 30-year-old accused has not been arrested yet.
As per the Maharashtra Police, the girl's mother works in a factory in the district and would drop her daughter at the child care centre, run by a woman, in Vasai before leaving for her workplace.
The husband of the creche owner has been booked for the crime under relevant sections of the IPC and the Protection of Children from Sexual Offences Act, said Deputy Superintendent of Police (Vasai) Vishwas Valvi.
The crime took place on November 22, but a complaint was filed by the victim's mother on Monday at the Valiv police station, it said.
The victim was the only girl going to the creche, Valvi said.