The Federal Security Service (FSB) did not identify the suspect or provide any details about his motive. The agency said in a statement carried by Russian news agencies that he organised and carried out the attack on his own.
The Islamic State (IS) group claimed responsibility for the blast, but a member of the security committee in the lower house of Russia's parliament cast doubt on the claim, saying it might have been an attempt by IS to gain publicity.
"Now, when the IS defeat in Syria seriously dented its image, it will try to restore its authority and claim responsibility for the attacks by others," Adalbi Shakhgoshev said, according to Russian news wires.
The FSB said it has handed over the suspect to the Investigative Committee, the nation's top investigative agency. The FSB normally deals with terror suspects itself, and the transfer could indicate that the man had other motives.
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.
Russian law enforcement agencies stopped short of immediately describing the supermarket blast as a terror attack, but President Vladimir Putin called it one on Thursday. He added that he ordered security agencies to kill terror suspects on the spot if they resist arrest.