According to latest reports, two people have been killed and over 15 people have been injured in police firing.
In Shimoga, protesters burnt 12 two wheelers, two tractors, two auto rickshaws and pelted stones, police said.
Prohibitory orders have been imposed in Shimoga and Hassan.
Hassan SP Sharat Chandra said the protest was against the article published in the newspaper.
Taslima in the article wrote that Mohammed Prophet was against burqa.
Seven persons have been arrested in connection with the incidents in Hassan, he added.
Additional DGP A R Infant said additional reinforcements have been sent to Shimoga.