The Central market has been a target of terrorist attacks twice: in 1999, when a car explosion killed 52 people, and in 2008, when a female suicide bomber detonated herself at the bus stop near the market, claiming the lives of 12 people and injuring 41.
A second bomb discovered in a car near the site of the first explosion was successfully defused.
Russia's president, Dmitry Medvedev, condemned the attack as "monstrous".
The prime minister, Vladimir Putin, said the attack was designed to "sow enmity between our citizens".
He called on Russia's substantial Muslim population to make a "decisive contribution" in the fight against extremism.