"The terrorist suspect had close ties with radical Islamist groups operating in Russia. These groups have already been under investigation by Russian security bodies," the source said.
The source declined to provide the names and details on origin of these groups.
A bomb explosion took place in the St. Petersburg metro on the stretch between Sennaya Ploshchad and Tekhnologichesky Institut stations at around 3 p.m. local time (noon GMT).
Russia's National Anti-Terrorism Committee (NAK) earlier said at least 11 people were killed and 45 others were wounded in the blast.
Russia's Investigative Committee has opened a criminal investigation into a suspected terrorist attack.