The couple had allegedly killed the 18-year-old on August 1 at their house at Goutami, the body was recovered from the canal at nearby Kaukhata on August 4, police said.
The accused - Runu Jena (45) and Saura Jena (52), mother and father of the deceased respectively were arrested and a murder case was registered against them, said sub divisional police officer of Berhampur Sadar, A K Mohanty.
Preliminary inquiry showed that the girl's mother slit her throat, while the father helped in disposing the body, he said.
The couple might have killed the girl when she refused to marry the person they had selected for her, police said.
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