The constable is attached to Mumbai's Byculla police station and hails from Dindori in the district, police said.
The girl is a resident of a village under Dindori taluka 75 kms from here, police station in-charge Madhukar Gavit said.
The accused has been identified as constable Gorakh Shekhare (25), police said.
The girl's parents lodged a rape complaint after the incident last night following which Gorakh was arrested, said Gavit.
Police refused to give details of the case citing the matter was still under investigations.