The girl, who is 15 years old, was travelling by the rickshaw from Kutad to Shirgaon when the driver took it to an isolated spot and raped her inside the vehicle, police said.
He also allegedly beat her up and warned her not to disclose the incident.
The case was first registered with the Vangaon police and later transferred to the Boisar police station.
Sub-inspector SD Malij of Boisar police station said no arrest had been made in the case yet, though the accused had been identified.