Islamic State has claimed responsibility for the explosion, according to SITE, a group that monitors IS statements.
The statement said the suspect organized and carried out the attack on his own.
On Wednesday evening, a homemade bomb placed in a locker at the supermarket in northwestern Saint Petersburg, Russia's second city and President Vladimir Putin's home town, went off sowing panic among customers and wounding 14 people including a pregnant woman.
Spokeswoman for the Investigative Committee Svetlana Petrenko said that investigators had begun questioning the suspect.
He said he had ordered the nation's security services to "act decisively" and "liquidate bandits on the spot" if armed militants put up resistance. The FSB normally deals with terror suspects itself, and the transfer could indicate that the man had other motives.
The Islamic terrorists claim they were behind the blast that rocked the Perekrestok market in northwest St Petersburg on Wednesday (27 December).
The Interfax news agency reported that the suspect was a 35-year old local resident who said he was a member of an occult movement and was taking drugs.
Shortly after the explosion, Russian President Vladimir Putin called the incident a terror attack.
Putin emphasized that Russia's two-year military campaign in Syria helped avert more terror attacks by eliminating militants who threatened Russian Federation.
Putin's 2015 decision to intervene in Syria militarily on the side of Bashar al-Assad has made Russian Federation a priority target for the Islamic State group. Fourteen people were killed and dozens more were injured on April 3 when a suicide bomber detonated explosives in the city's metro system.
Putin said following the explosion: "I have instructed the director of the Federal Security Service to act within the framework of the law during detention (of suspected terrorists)".