Police reportedly killed the shooter.
Four people remained in hospital after Sunday's attack, including two women in serious condition, the regional health ministry said.
The Russian Christian Orthodox Church criticised the attack in Kizlyar as a "monstrous crime" that, coming on the eve of the Lenten fast, was a "provocation created to stoke religious tensions between Orthodox Christians and Muslims" in Dagestan.
A statement from the Islamic State (ISIS) terror group, posted Monday on an ISIS-affiliated website, claimed responsibility for the shooting, saying a Muslim fighter attacked "a Christian temple" in Kizlyar.
The attacker was "eliminated " by police fire, the statement added.
"We must think of how to educate our youth, because the attacker was a very young person but already deeply confused in his views", said Orthodox Archbishop Varlaam, a top-ranking cleric in the region who led the service.
Dagestan, bordering Chechnya, is one of the poorest and most unstable regions of Russian Federation and has struggled against an Islamist insurgency.
"People were leaving a church after an evening service when he opened gunfire at them", Shuvalov told TASS.
It has been the scene of an Islamist insurgency following separatist wars in neighbouring Chechnya.