A police spokesman said in Panaji that the lady was alone in her residence where the incident took place.
"The incident happened between Saturday night and Sunday morning," he said, adding that a complaint was lodged by the lady's nephew at the Old Goa police station.
The name of the lady has been withheld by the police, while a manhunt is on to trace those behind the gruesome act.
The lady was allegedly raped and later murdered, by smothering her face with a soft object, the police said.
Image: A protest against growing number of rapes