In a video posted on the social media recently, the man, who identified himself as Krishnakumaran Nair, was purportedly heard saying that he had decided to return to India from the Gulf to kill the CPI(M) leader and attack his family, the police said.
In the video, Nair also allegedly hurled expletives at the chief minister, his family and some of his ministerial colleagues, they added.
After the video was shared on the social media, the accused posted another video, apologising to Mr Vijayan, his family, state Electricity Minister MM Mani and the Keralite community, saying his remarks in the earlier video were made in an inebriated state, the police said.
The case against Nair was registered under IPC section 500 (punishment for defamation) and relevant sections of the Kerala Police Act.
The case was lodged suo motu by the police at the Central police station, Ernakulam.