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.