A 22-year-old woman was killed and 14 other people injured when explosions ripped through two coaches of a train minutes after it pulled into one of India's busiest railway stations, officials said.
Police said they were questioning one suspect after the double blast at Chennai station, but there were no further details.
Prime Minister Manmohan Singh condemned the attack, saying "such barbaric acts targeting innocent men, women and children only highlight the desperation and cowardice of those responsible".
There was no immediate claim of responsibility in a region of India considered relatively peaceful.
Authorities suspect the blasts were caused by bombs planted on the Bangalore-Guwahati Express train, said M Bhupati, spokesman for India's southern railway system.
"The police are already on the job, they are investigating what kind of bomb it was and what was the purpose," RK Mishra, general manager of Chennai Central Station, told reporters.
The explosions come amid heightened security nationwide for India's massive general election, which is held in phases over several weeks.
At least one of the blasts erupted from underneath a seat where the 22-year-old woman was sitting, killing her, Mr Mishra said. Fourteen people were taken to hospital but none of the injuries was serious, said G Muthuraj, a spokesman of the Rajiv Gandhi General hospital in Chennai.
India has one of the world's largest railway networks with more than 23 million passengers a day travelling on about 11,000 trains. Every day, hundreds of thousands of commuters and long-distance passengers use the railway station in Chennai, one the country's busiest.
The train originated in Bangalore and was headed to Gauhati, the main city in the remote north-eastern state of Assam.
K Ramanujam, Tamil Nadu's director-general of police, said a special investigation team comprising forensic experts and police will investigate the blasts.
"It is premature to speculate what kind of device was used in the blast. The damage to the train is not heavy," he said.