Another 45 people were injured in the explosion between two subway stations on April 3.
The Interfax and Tass news agencies said the suspect had been identified, but there are conflicting reports as to whether he was a suicide bomber.
Meanwhile, St Petersburg authorities have declared three days of mourning.
President Vladimir Putin, who was in his home city when the explosion occurred, visited the scene and laid flowers at a makeshift shrine.
Russian investigators have given few details. No group has said it was responsible.
World leaders rallied behind Russia in condemning the blast.
The White House said President Trump had spoken to President Putin by phone and offered “full support” in bringing those responsible to justice.
A statement said: “Both President Trump and President Putin agreed that terrorism must be decisively and quickly defeated.”
German Chancellor Angela Merkel described the attack as a “barbaric act” and EU foreign policy chief Federica Mogherini said Europe’s thoughts were with the Russian people.
First images from the scene showed a train at Tekhnologichesky Institut station with a hole blown in its side and wounded passengers on the platform.
Initial reports suggested there had been two explosions, one each at Sennaya Ploshchad and Tekhnologichesky Institut stations.
However, the Russian National Anti-Terrorist Committee later confirmed there had been only one explosion, between the two stations, at about 14:30 local time.
Senior investigator Svetlana Petrenko told Russian media the train driver’s decision to continue to the next station almost certainly helped save lives, as it allowed people to be rescued quickly.
Health Minister Veronika Skvortsova said 10 people had died – seven at the scene, one in an ambulance and two in hospital. The death toll was later raised to 11.
Andrei Przhezdomsky, the head of the National Anti-Terrorist Committee, said the blast was caused by “an unidentified explosive device”.
The discovery of an explosive device at another station, Ploshchad Vosstaniya, also suggested a co-ordinated attack.
Interfax said the focus was now on a 23-year-old man from Central Asia known to have links to radical Islam.
The news agency said the man died in a suicide blast and was identified through his remains.
However, President Putint’s spokesman Dmitry Peskov would not comment on reports a suicide bomber was to blame.
Tass reported that a woman may also have been involved in the attack.
St Petersburg’s subway system, which is used by more than two million passengers every day, has not suffered previous attacks.
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