The writer, who insists that he is not attached to any party and that he has been critical of the Congress as well, received some unpleasant calls after the BJP-led NDA's victory last week.
Mr Ananthamurthy has now been provided with police protection and two constables have been deployed round-the-clock outside his residence.
The writer told NDTV, "By a slip of tongue, because of emotion, I said I would not like to live in a country ruled by Modi. I corrected it but they held on to it."
After the BJP's victory last week, the threatening phone calls started, amid reports that the Jnanpith Award winner had even been sent a one-way ticket to Karachi.
"I would get phone calls asking me, 'when are you leaving'? I did not get tickets to Karachi - I would like to visit Pakistan, but for another reason! I have friends there who love India," said Mr Ananthamurthy.
Bangalore's Police Commissioner Raghavendra Auradkar told NDTV, "As a precautionary measure, as soon as the results were announced, we had posted one or two policemen to avoid any untoward incidents because emotions would be running high at that time. Dr Ananthamurthy spoke to me and said he doesn't want such a huge number of policemen. It is a waste of manpower because police are supposed to serve common citizens."
The 81-year-old writer says he is not frightened by the calls and does not pay attention to jibes on social networks.
"I am not on Facebook - people have told me not to see it," he said.
So he will continue to express his point of view: whether it is his concern about the lack of a strong opposition in Parliament, the role that corporate houses will play or even sympathy for Mr Modi, who, he says, will have his task cut out while choosing his cabinet.
Meanwhile, the BJP has officially distanced itself from the incident and asked people not to bother Mr Ananthamurthy.