The Tass and Interfax agencies reported the blasts hit the Sennaya Ploschad and nearby Tekhnologichesky Institut stations in the centre of the city.
Images posted on social media showed a carriage in Sennaya station with its doors blown out with casualties nearby.
President Vladimir Putin said all causes, including terrorism, were being investigated.
President Putin was in St Petersburg earlier on Monday but is now outside the city, his spokesman Dmitry Peskov said.
"I have already spoken to the head of our special services, they are working to ascertain the cause," he said, at a meeting with Belarus President Alexander Lukashenko.
Interfax reported that at least 20 people had been injured, and that one of the blasts may have involved a device filled with shrapnel.
Moscow metro officials said they were introducing extra security measures as a result.
Tekhnologichesky Institut serves metro lines one and two, with the first hall opening in 1955, followed by the second in 1961.
Sennaya Ploschad - the next station along metro line two - opened two years later, in 1963.
____________________________________________________________Длительность: 3:34Тэги для этого Видео: 2016 Blue Global BBC World BBC Russia killed died victims death deaths St. Petersburg Saint Petersburg metro train platform explosion blast smoke bloody blood President Russian Vladimir Putin Putin Vladimir carriage Sennaya station Ploshchad Institute of Technology