Patrolling and vigil at busy junctions, including railway station, airport and bus terminals, has been beefed up as a precautionary measure, police said.
Vehicles entering the city from other states are being subjected to thorough checks, they said.
At the Chennai Central Railway station, which attracts thousands of passengers daily, the police is checking vehicles parked in parking lot and also those entering there.
Police have pressed sniffer dogs into service and baggages of passengers were also being screened.
Hawk eye was being maintained on CCTV network installed at various locations to prevent any untoward incident, police said.
The bomb, apparently strapped to the motorbike with a Tamil Nadu registration plate parked between a van and a car, went off around 10.30 AM about 100 metres diagonally opposite BJP office in Malleshwaram.