Six other people were injured in the blast at around 12:45 (08:45 GMT), an official said. The cause is unclear.
A suspected female suicide bomber killed at least six people when she attacked a bus in the city in October.
An Islamist insurgency in the North Caucasus region has led to many attacks there in recent years. Insurgents have also attacked big Russian towns.
Volgograd lies about 900km (560 miles) south of Moscow and 650km north of the North Caucasus.
Russian authorities are concerned militant groups could be ramping up violence in the run up to the the 2014 winter Olympic Games in the city of Sochi, which is due to start on 7 February.
No group claimed immediate responsibility for Sunday’s explosion.
In July, Chechen insurgent leader Doku Umarov posted an online video urging militants to use “maximum force” to prevent the Games from going ahead.
Volgograd lies about 690km north-east of Sochi.