The defence ministry said it believed the reason for the crash was equipment failure, the TASS news agency reported.
The crash occurred at 3.42pm (12.42pm GMT) during a training flight, and the helicopter was flying without weapons, Russian news agencies cited the defence ministry as saying in a statement.
An investigation was opened to confirm the cause of the crash, which occurred in the Dzhankoi region of northern Crimea.
Russia annexed Crimea from Ukraine in 2014. The peninsula is internationally recognised as part of Ukraine and Kyiv has vowed to regain control over it.
Military sites and fuel depots across Crimea have been targeted several times in drone attacks since Russia invaded Ukraine last February, including two weeks ago in an attack on an oil storage facility in Sevastopol.
Ukraine does not usually take public responsibility for the incidents, but officials often post cryptic comments online or appear to celebrate major strikes.