The Sennaya Square station in the city center was cordoned off on Tuesday, and commuters were told via an announcement that three more stations have also been closed down.
Earlier on Tuesday Russia's health minister, Veronika Skvortsova, said the death toll had risen to 14. Forty-nine people are still in hospital.
Kyrgyzstan's State Committee for National Security said in a statement it believed one suspect behind the bombing was a Kyrgyz-born Russian citizen it identified as Akbarzhon Dzhalilov, the Independent reported.
Russian media said authorities believed the 23-year-old suspect was linked to radical groups.
Russia's state investigative committee said the bomb may have been detonated by a man whose body parts were found in one of the train carriages. It declined to give the man's name, in contrast with its Kyrgyz counterpart.
"It has been ascertained that an explosive device could have been detonated by a man, fragments of whose body were found in the third carriage of the train," the committee, which has sweeping powers, said in a statement.
"The man has been identified but his identity will not be disclosed for now in the interests of the investigation," the statement added.
US President Donald Trump called the attack "a terrible thing" and added: "Happening all over the world."
Putin said authorities were investigating the possibility terrorism was the motive for the bombing.
His spokesman, Dmitry Peskov, told reporters on Tuesday the fact the Russian president was in the city when the bomb went off, though several dozen miles away from where he was hosting talks, "makes one pause" and is "something for the intelligence agencies to analyze."