At least 45 people were injured in the explosion between two underground stations on Monday afternoon.
Another explosive device was found and made safe at a station nearby.
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.
Authorities in Saint Petersburg have declared three days of mourning for the victims.
President Vladimir Putin, who was in the city when the blast occurred, visited the scene on Monday evening and laid flowers at a makeshift shrine.
