Among the dead is militant group leader Bammatkhan Sheikhov, who is suspected of plotting an attack on a Russian military base in 2010, RIA Novosti said.
"The active phase of the special operation is complete. During the fight, special forces killed nine militants, including the odious leader Bammatkhan Sheikhov," Russia's Anti-Terrorism Committee said in a statement.
The government didn't say what led them to the apartment where the shootout took place but local media reports indicate officers were tracking the suspects and cornered them in an apartment where the fight took place. Homes and businesses in the area were evacuated.
Two police officers were injured during the incident, RIA Novosti said.
The raid continues what's been a particularly bloody few days in the Russian province. Six other suspected militants were killed over the weekend.
Dagestan has become a hotbed of separatist Islamist hostility, much of it dating to conflicts in neighboring Chechnya in the 1990s, RIA Novosti said.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff