A 22-year-old woman passenger, identified as Swathi, bound for Guntur via Vijaywada, was killed in the explosions that occurred in the S4 and S5 coaches in quick succession.
The injured, including two grievously hurt, have been rushed to the state-run Rajiv Gandhi Hospital, where doctors said the injured were "out of danger".
The train arrived from Bangalore for a ten-minute halt at the Central Railway station, the major railway hub in this metropolis, at about 7.05 AM, and the explosions occurred in the coaches at about 7.15 AM.
Police said a suspect has been detained in connection with the explosions and he was being questioned.
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Tamil Nadu DGP K Ramanujam said a special investigation team would investigate the blasts and added that Chennai was not the target.
"It is not a major blast. It is suspected that Chennai could not have been target of those who were behind the blast because the train was running late. Some other location could have been the target", Ramanujam said.
Southern Railway General Manager Rakesh Mishra described it as a "minor blast".
Railway Minister M Mallikarjun Kharge, expressing shock over the incident, announced Rs one lakh ex-gratia to the family of the woman killed in the explosion.
He said Rs 25,000 will be given to those seriously injured and Rs 5,000 to those with minor injuries.
Kharge said the Railway will bear the entire treatment expenses of the injured.
Home Minister Sushilkumar Shinde, who is in Himachal Pradesh for campaigning for Congress candidates, said, "I have directed my officials to provide all assistance to the state government".