The incident took place late Sunday night, they said, adding that she had attended a marriage party.
After the event got over, her cousin Mukesh Samka took her to a nearby field where he allegedly raped her.
She died of severe injuries to her private parts, they said yesterday.
When the girl failed to return home, her family members started searching for her and they found her dead body near a well in the vicinity of their house.
Members of the marriage party were questioned and they told the police that she had gone with Samka.
"We have interrogated Samka and will arrest him soon. He has been booked under sections 376 (rape) and 302 (murder) of the Indian Penal Code," Dahod (taluka) PSI M M Puwar said.
Photos: 'Rock On 2' stars Farhan, Shraddha on 'Yaaron Ki Baraat'
Photos: Ajay Devgn launches 'Shivaay' comics at Mumbai Comic Con
Photos: WWE star Sheamus and John Abraham clash in Mumbai
Umesh Yadav's birthday: Indian cricketers and their tales of struggle
Photos: Raveena Tandon, husband Anil Thadani's dinner date in Bandra