Police spokesman Vyacheslav Gasanov said the bomber blew herself up in the central square in the provincial capital, Makhachkala. He did not give details about the injured children.
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 neighbouring Chechnya.
The bombers are often called "black widows" in Russia because many are the widows, or other relatives, of militants killed by security forces.
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, who was killed a shootout with police days after the 15 April bombings, spent six months in Dagestan in 2012.
Dagestan remains an epicentre 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
Human rights groups accuse security agencies of abductions, torture and extrajudicial killings of civilians that further fuel the confrontation with Islamic radicals.