The bomber detonated an explosives-laden belt in the central square in the provincial capital, Makhachkala, Dagestan's police spokesman Vyacheslav Gasanov said.
The bomber was identified as Madina Alieva, who married an Islamist who was killed in 2009 and then wedded another Islamic radical who was gunned down last year, police spokeswoman Fatina Ubaidatova said.
Since 2000, at least two dozen women, most of them from the Caucasus, have carried out suicide bombings in Russian cities and aboard trains and planes. All were linked to an Islamic insurgency that spread throughout Dagestan and the predominantly Muslim Caucasus region after two separatist wars in neighboring Chechnya.
The bombers are often called "black widows" in Russia because many are the widows, or other relatives, of militants killed by security forces. Islamic militants are believed to convince "black widows" that a suicide bombing will reunite them with their dead relatives beyond the grave.
Police said two of the people injured in the attack were in a critical condition. There were no details about the injured children.
The Tsarnaev brothers suspected of carrying out last month's Boston marathon bombings, are ethnic Chechens who lived in Dagestan before moving to the United States. Tamerlan Tsarnaev, the elder brother who was killed a shootout with police days after the April 15 bombings, spent six months in Dagestan in 2012.
Dagestan remains an epicenter of violence in the confrontation between radical Islamists and federal forces.
This week, a double explosion in Makhachkala killed four civilians and left 44 injured, while three security officers and three suspected militants have been killed in other incidents.
Islamists strive to create an independent Muslim state, or "emirate," in the Caucasus and parts of southern Russia with a sizable Muslim population.
Although Chechen separatists were battered almost a decade ago, Islamists continue to move through the region's mountains and forests with comparative ease despite security sweeps by federal forces and police under the control of local leaders loyal to the Kremlin.
Human rights groups say that abductions, torture and extrajudicial killings of young men suspected of militant links by Russian security forces have helped swell the rebels' ranks. Caucasus experts say that Islamists routinely extort money from government officials and businessmen and attack or kill those who refuse to pay.
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