The Tamil Nadu Police detained a person for questioning. Authorities suspect the blasts were caused by bombs planted on the train, said M Bhupati, spokesperson of Southern Railway.
Condemning the blasts, Prime Minister Manmohan Singh said such "barbaric acts" highlight the "desperation and cowardice" of those responsible. He asserted that no efforts would be spared in bringing the perpetrators to justice.
Tamil Nadu chief minister and AIADMK leader J Jayalalithaa ordered a Crime Branch-CID probe, while the opposition DMK slammed the state government over law and order.
The woman killed in the blasts was identified as Swati, a 24-year-old engineer who had recently joined a leading software firm TCS in Bangalore. She was supposed to tie the knot after two months.
The first explosion took place around 10 minutes after the Guwahati-bound train, running one and a half hours late, chugged into platform number nine at Chennai Central around 7am. The second blast was heard within a few seconds.
"They were not major blasts. It is suspected that Chennai was not the target as the train was running late," Tamil Nadu director general of police K Ramanujam said.
Prasanna Darnal, a 20-year-old nursing student on board, said, "It was like a small Diwali bomb going off. There were shrieks and cries of people and everyone was rushing to get out of the train."
Southern Railway general manager Rakesh Misra told reporters the blasts took place in S4 and S5 sleeper coaches.
The injured, including two hurt seriously, were rushed to a state-run hospital, where doctors said they were out of danger.
The train started for Guwahati again at 12.15pm, after the affected bogies were replaced.
Passengers were allowed to continue with the journey after thorough verification of their identities. They had to submit their contact details for future reference.
Security at the railway station was beefed up. Baggage screening procedures were also scaled up. As a precautionary measure, the police strengthened vigil at the Chennai airport.
Union railway minister M Mallikarjun Kharge announced Rs. 1 lakh compensation for the family of the deceased.
He said Rs. 25,000 each will be given to those seriously injured and Rs. 5,000 each to those with minor injuries. Kharge said the Indian Railways will bear the medical expenses of the injured.
"The security agencies must be allowed to do their job. It is not fair to interfere in the police investigation," Kharge added.
CM Jayalalithaa too announced Rs. 1 lakh for Swati's family. She added Rs. 50,000 each and Rs. 25,000 each will be given to the passengers with serious and minor injuries, respectively.
"I strongly condemn the blasts. I have directed the police to coordinate with Railway Police to nab those behind this incident and initiate legal action against them. I have asked the CB-CID to probe this incident," she said in a statement.
Meanwhile, the Centre was reportedly forced to put on hold sending teams of the National Investigation Agency (NIA), National Security Guard (NSG) and forensic experts to Chennai.
Strongly opposed to any interference from central agencies on law and order, Jayalalithaa refused to take any help from the Centre, some media reports said.
Home minister Sushilkumar Shinde said he had directed officials to provide all assistance to the state government.
Railway authorities set up helplines to provide information to the public in Chennai and Bangalore.
The Chennai helplines are 044-25357398 and 044-64502416 and in Bangalore the number is 080-22876288.