There was no immediate information on whether the car which blew up in Vladikavkaz had been rigged with explosives or if the blast was due to other causes.
The market and its surrounding streets have been the target of several bomb attacks over the past dozen years, in which scores of people have died.
Vladikavkaz is the capital of the Russian republic of North Ossetia. Although it is less plagued by violence than some other republics in the region such as Chechnya and Dagestan, North Ossetia suffers ethnic tensions.
It also was the scene of the 2004 Beslan crisis, in which Chechen terrorists took hundreds of hostages at a school – a siege which ended in a bloodbath, killing more than 330 people, around half of them children.
Today’s explosion happened in a lane near the market at around noon, said Oleg Rudenkov, of the North Ossetian Emergencies Ministry. Republican Interior Ministry spokesman Nikolai Morozov said five people died and at least 20 were wounded.
The Vladikavkaz market was bombed in 1999 and 55 people died. Another bombing in 2001 killed six people. In 2004, 11 people died when a minibus stopped near the market was bombed.
In Dagestan, officials said today that a hotel employee and another civilian were shot dead by men trying to build a bomb in their hotel room.
Republican Interior Ministry spokesman Vyacheslav Gasanov said the shooting took place in the capital, Makhachkala, late yesterday.
He said three armed men fled a room in the small hotel after an explosion and opened fire on a hotel clerk and another person who confronted them. He said police found several bombs and six grenades in the room.
In the Dagestani town of Khasavyurt, on the border with Chechnya, a policeman returning home from work was also shot dead, Mr Gasanov said.
Dagestan is plagued by near-daily shootings and explosions blamed on criminal gangs and on militants inspired by the insurgency in neighbouring Chechnya.