Regional officials said the woman set off her charge near the metal detectors stationed at the entrance to the city's main train station while it was packed with afternoon travellers.
Footage on Russian state television showed windows blown off across the top two floors of the grey brick building and numerous ambulances gathered at the station's front entrance amid piles of debris and snow.
"Initial indications are that the blast was set off by a female suicide bomber," the National Anti-Terror Committee said in a statement.
Russia's Investigative Committee spokesman Vladimir Markin said officials had launched an inquiry into a suspected "act of terror".
A regional government spokesman told the RIA Novosti news agency that at least 18 people were killed and more than 40 injured in the attack.
But a federal health ministry spokesman told Russian state television that the number of people wounded stood at more than 50.
The city of Volgograd -- known as Stalingrad in the Soviet era -- was already attacked in October by a female suicide bomber with links to Islamists fighting federal forces in Russia's volatile North Caucasus.
The October 21 strike killed six people aboard a crowded bus and immediately raised security fears ahead of the February 4-23 Winter Games in Sochi.
The Black Sea city lies 690 kilometres (425 miles) southwest of Volgograd and in direct proximity to the violence ravaging North Caucasus regions such as Dagestan and Chechnya on a daily basis.
Militants are seeking to impose an Islamist state throughout Russia's North Caucasus. Their leader Doku Umarov has ordered his footsoldiers to target civilians outside the region and disrupt the Olympic Games.
The Sochi Games' success carries heavy political overtones for the Kremlin amid its efforts to use patriotism to mobilise support for President Vladimir Putin's 14-year rule.
Putin staked his personal reputation on the Games' success by lobbying for Sochi's candidacy before the International Olympic Committee and then spending more than $50 billion (36 billion euros) for the event.
Russian authorities have repeatedly vowed to take the highest security precautions in Sochi, and there have been few indications to date of foreign sports fans cancelling their attendance out of security fears.
Female suicide bombers are often referred to in Russia as "black widows" -- women who seek to avenge the deaths of their family members in North Caucasus fighting by targeting Russian civilians.
Female suicide bombers set off blasts at two Moscow metro stations in March 2010 that killed more than 35 people.
So-called black widows were also responsible for taking down two passenger jets that took off from a Moscow airport within minutes of each other in 2004, killing about 90 people.