The attack occurred in the village of Kizlyar in Dagestan, agencies said.
The Islamic State claimed responsibility for the shooting, its news agency Amaq reported, but did not provide immediate evidence for the claim.
The small republic in the Caucasus mountains borders Chechnya, where Moscow has led two wars against separatists and radical religious groups since the 1991 Soviet collapse and which has seen a large number of people join the Islamic State.
Russian news agencies said the attack occurred as churchgoers celebrated Maslenitsa, a Christian holiday marking the last day before Lent.
The assailant was identified as a 22-year-old man local to the region, the TASS news agency said, citing the investigative committee.
He was shot and killed by security services who were on duty nearby, TASS said, adding that a hunting rifle, bullets, and a knife were discovered on his person.
Initial reports suggested all five victims were women, TASS said, citing the local branch of the interior ministry.
The injured include two members of local security services and two civilians, also women, the Interfax news agency said.