Russian investigators opened a probe into an "act of terror" and officials said the blast appeared to have been triggered by a suicide bomber in a car at the entrance to the market.
"The headless body of the presumed terrorist was found in the car which exploded opposite the central market," Taimuraz Mamsurov, the head of the North Ossetia region of which Vladikavkaz is the capital, told ITAR-TASS.
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The bombing created carnage around the market, with several cars reduced to wreckage by the blast and charred corpses laid out on stretchers, an AFP correspondent at the scene reported.
The attack was the latest strike to hit the Caucasus region, plagued by an Islamist-inspired insurgency.
President Dmitry Medvedev ordered his envoy for the Russian North Caucasus region, Alexander Khloponin, to urgently fly to Vladikavkaz, the Kremlin press service said.
The ITAR-TASS news agency said that the power of the blast shattered windows of nearby buildings.
At least 11 people were killed and more than 60 wounded, the deputy health minister of North Ossetia, Taimuraz Revazov told reporters.
Mamsurov told Interfax that it is believed the suicide bomber drove up to the entrance of the market in a Volga 3102 car before igniting his charge.
North Ossetia lies in Russia's troubled Northern Caucasus region, north of the Georgian breakaway region of South Ossetia over which Moscow and Tbilisi fought a war in August 2008.
It is the only majority Christian region in Russia's largely Muslim North Caucasus and neighbours the Muslim region of Ingushetia which has been beset by deadly attacks over the last months.
Interfax said the blast had been caused by explosives weighing 10 kilogrammes of TNT equivalent. ITAR-TASS said there was panic at the market amid fears there could be a second explosion.
"A second threat is not ruled out and at the current moment the perimeter of the market and nearby roads is being encircled," a local interior ministry spokesman told ITAR-TASS.
It said the explosion went off at the entrance to the market, which is usually crowded as it is where employers recruit potential employees.
Although it has seen increasing unrest over the past years, North Ossetia has traditionally been more stable than the Muslim regions of the North Caucasus.
In November 2008, the mayor of the city was killed when an assassin shot him in the chest near his home.
Russia has been on a state of high alert after the double bombings carried out by two female suicide bombers on the Moscow metro on March 29 killed 40 and wounded more than 100.
The Kremlin fought two wars against separatist rebels in Chechnya in the 1990s but the insurgency has now become more Islamist in tone and has spread to neighbouring Ingushetia and Dagestan.
