Russia's TASS news agency reported that one person died in the resort town of Sochi, another in Russian-controlled Crimea and a third on a ship in the Kerch Strait, which separates Crimea from the Russian mainland.
Storms have been ravaging the Black Sea region since Friday.
A video posted online showed high waves sweeping through the Sochi resort's waterfront and swept cars away. Streets in the city of Yevpatoriya in Crimea were flooded.
The Russian-appointed governors of Crimea and Sevastopol declared a state of emergency.
Russia's Emergency Services Ministry said it had evacuated more than 350 people.
The Energy Ministry also said that bad weather on Monday morning caused power outages for about 1.9 million people in the southern Russian regions of Dagestan, Krasnodar and Rostov, as well as Crimea.
Neighboring Ukraine is also being swept by a snowstorm that has knocked out power to more than 2000,<> towns and blocked highways.