An unidentified gunman fired at worshippers at the church in the town of Kizlyar, local press reports said.
"At about 16:30 [13:30GMT], an unknown man opened fire using a hunting rifle," the regional internal affairs ministry statement said.
"As a result, four people were killed and four injured. Among the wounded are two members of the security forces. The gunman was killed."
A fifth woman died of her injuries in hospital, health ministry spokeswoman Zalina Mourtazalieva told TASS news agency.
Two Russian police officers were injured in the attack.
According to a local official, the assailant was a local man in his early twenties, the Interfax news agency reported.
The Daesh terror group claimed responsibility for the attack via the Telegram messaging app.
A spokesman for Russian Orthodox Patriarch Kirill strongly condemned the attack, branding it a "monstrous crime" aimed at "provoking a confrontation between Orthodox Christians and Muslims" in the North Caucasus.
Images published by the local press showed the body of a bearded man dressed in military fatigues who was identified as the assailant.
Next to his corpse lay two of his victims, covered in a white shroud.
Dagestan, bordering Chechnya, is one of the poorest and most unstable regions of Russia.
Some extremists from the region, which lies immediately east of Chechnya, are known to have traveled to Syria to join Daesh.
In 2015, Daesh declared it had established a "franchise" in the North Caucasus.
It has claimed a number of attacks on police in Dagestan in the last couple of years that have involved guns and explosives, as local security forces battle a simmering insurgency.
Sunday's shooting comes exactly one month before the March 18 presidential election that Vladimir Putin is almost guaranteed to win.
