The bomber blew herself up not far from the interior ministry building in the centre of Makhachkala, spokeswoman Fatina Ubaidatova told AFP.
The Moscow-based Investigative Committee said an unidentified woman came up to traffic policemen and detonated an explosive.
All the injured were hospitalised. Five were policemen and two of them were in a "critical condition", Ubaidatova said.
The suicide bomber herself died. State television broadcast a picture of a young woman, her head covered with a scarf, suggesting she might have been behind the bombing.
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Dagestan is one of Russia's most violent regions.
It experiences almost daily shootings and bombings that officials blame on local criminals and Islamists with links to Chechnya, where over the past 20 years the Kremlin has fought two wars.
The region is also home to the parents of Boston marathon bombing suspects Dzhokhar and Tamerlan Tsarnaev.