Valanka Alemao, a Congress politician, is the daughter of former Goa chief minister Churchill Alemao.
The case was lodged on a complaint filed by her mother, Fatima.
"An offence has been registered under section 66 (a) of the Information Technology Act and other relevant sections of the Indian Penal Code," an officer at the Colva police station said.
In pictures: A look at Anil Kumble's illustrious cricket career
Photos: Karisma Kapoor, Preity Zinta, Shraddha Kapoor at Mumbai airport
Spotted: Anushka Sharma and Diljit Dosanjh at Mumbai studio
Photos: Mallika Sherawat at a restaurant in Bandra
Photos: Tina Ahuja, Gizele Thakral at a calendar launch