Interfax reports that five people have died as a result of the incident.
"At about 16:30 [13:30GMT], an unknown man opened fire using a hunting rifle", the regional internal affairs ministry statement said.
The victims were churchgoers leaving a service in Russian Federation. Five people were killed and at least five people were injured, including two police officers.
The Takfiri Daesh terrorist group claimed responsibility for the attack on the Telegram messaging app. "I believe God saved us, not allowing the man to get inside the church", the woman told the news outlet.
"He was carrying a rifle and a knife", he added. "He is a local resident of 22 years of age".
"People were leaving a church after an evening service when he opened gunfire at them", an official said, Fox reported, citing local news outlets.
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The government has released hundreds of political detainees this year in steps it says are meant to "widen the political sphere". Nonetheless, the span of the condition of the crisis was not uncovered in the communicated, the Anadolu news office revealed.
Next to his corpse lay two of his victims, covered in a white shroud.
The motive for the shooting is not known.
In 2015, IS declared it had established a "franchise" in the North Caucasus. ISIS has claimed credit for the attack.
It has been the scene of an Islamist insurgency following separatist wars in the neighbouring Chechnya.
Russian President Vladimir Putin fired, three months ago, head of Dagestan Ramazan Abdulatipov and appointed Vladimir Vasilyev.