The operation in the town of Khasavyurt started Thursday morning when police and security service troops surrounded a building on the premises of a former brick plant where a militant group was holed up.
The HQ spokesman said associates of the militants had detonated an explosive device trying to help the besieged but nobody was killed.
One civilian was killed during the operation after climbing the roof of a nearby building. Two Federal Security Service officers were slightly wounded.
Daghestan borders Chechnya, which was a scene of violent battles between Islamic separatists and federal troops in the 1990s and early 2000s as the Kremlin tried to regain control over the republic. Although the active phase of all-out counter-terrorist operations in Chechnya ended years ago, sporadic clashes with small militant groups in this and neighboring republics are not uncommon.