Police said an FIR was registered against Ms Karandlaje on charges of provoking people to cause riots, disturbing communal harmony and spreading rumours.
Ms Karandlaje had tweeted about the recent rape and murder of the 15-year-old girl and accused Chief Minister Siddaramaiah of inaction to catch the 'Jihadis' behind the incident.
CM @siddaramaiah's appeasement politics has turned Karnataka into a safe haven for Jihadi Goons.He is shamelessly pursuing his agenda of appeasement & dividing the society.- Shobha Karandlaje (@ShobhaBJP) December 14, 2017
In a tweet about another incident she said "Jihadis tried to rape and murder a girl studying in 9th std near honnavar. Why is the govt silent about this incident? Arrest those who molested and injured this girl. Where are you CM @siddaramaiah?"
Police said the MP's tweets and video messages through social media platforms further added to tension in the regions of coastal Karnataka, which was on the boil since December 6 when 19-year-old Paresh Mesta was found dead under mysterious circumstances.
Ms Karandlaje meanwhile shared copies of the FIR on Twitter, saying "Govt which has failed in providing safety to women in Karnataka now tries to stifle my voice through a FIR. @siddaramaiah Govt protecting Jihadis."
She vowed to continue her fight against 'Jihadi elements' without succumbing to the pressure of the Chief Minister.
Protesting against the girl's murder, right wing outfits called a bandh in Talikote, Vijayapura and Chikkamagaluru today. Security was beefed up in these areas, police said.