The cause of the blast was not immediately clear. An attack by a female suicide bomber in the same Russian city on October 21 killed seven people.
If the explosion is found to have been another strike by Islamist militants, it will bolster fears of attacks as Russia prepares to host the 2014 Winter Olympics in the Black Sea resort city of Sochi in less than six weeks' time.
On Friday, a car bomb killed three people in the southern Russian city of Pyatigorsk.
Volgograd is a city of around 1 million people, about 430 miles (690 km) northeast of Sochi.
It lies close to Russia's North Caucasus, a strip of mostly Muslim provinces plagued by near-daily violence in a long-running  Islamist insurgency. Insurgent leader Doku Umarov, a Chechen warlord, urged militants in a video posted online in July to use "maximum force" to prevent President Vladimir Putin staging the Olympics.
There was no immediate claim of responsibility after Sunday's explosion.


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