"We have received an SMS at our traffic control room threatening the life of the chief minister. We are investigating it," city police commissioner T Rajendran told reporters in Chennai at a media briefing.
When asked about the details of the message, he said the SMS stated that the chief minister would be killed in a bomb attack.
To a question on Karunanidhi and All India Anna Dravida Munnetra Kazhagam chief Jayalalithaa receiving threatening letters recently, he said the police was not taking the issue lightly.
"We are taking it seriously. We keep investigating all the threat cases. We will crack it very soon," he said.
"E-mail threats have some technical issues, which would take some time to solve."
Meanwhile, elaborate security arrangements were being made for the festive season at important places in the city.
More CCTVs would be installed at vital places in the city, while watchtowers will also be set up at popular shopping places, Rajendran said.
Security would also be enhanced at the Central and Egmore railway stations to monitor passengers, he added.