The news regarding her killing is "shocking", he said in a Facebook post.
The chief minister said the incident has taken place at a time when progressive secular thoughts were getting strengthened in Karnataka and added that Lankesh was killed in a manner similar to that of M M Kalburgi.
Lankesh, in her 50s, had ample faith in secularism and was a fearless mediaperson, he said.
The chief minister hoped that those behind the killing would be brought to book as early as possible by the Karnataka government.
Lankesh, an outspoken critic of Hindutva politics, edited a Kannada tabloid 'Gauri Lankesh Patrike' besides owning some other publications.