There were eight known survivors, Russian media quoted emergencies ministry officials as saying.
Thirteen tourists, including a child, and three crew were on board when the Mi-8 crashed and sank in Kurile Lake on the Kamchatka Peninsula.
The helicopter is lying at a depth of 137 metres (450ft) - too deep for divers to operate, the officials say.
The aircraft belonging to the Vityaz-Aero company crashed about 700 metres from the shore, the emergencies ministry said, adding that specialist deep-water equipment was expected to arrive shortly.
Tourist Viktor Stvolkin, one of the survivors, later gave a dramatic account of how he had managed to escape from the sinking aircraft.
He was quoted by Russia's Ria Novosti news agency saying that he was asleep during the flight and only woke up when "the water hit my face in a stream".
"My friend's son was sitting next to me. He was fastened with seat belts, and I did not have time to pull him [free]. I only managed to unfasten myself."
Mr Stvolkin added that he had managed to escape through the cockpit's smashed window from a depth of about eight or nine metres.
According to preliminary information, the aircraft was travelling from the village of Nikolayevka to the Kuril Lake and the Khodutka volcano when it crashed, the emergencies ministry said.
The Mi-8 - a medium twin-turbine helicopter - was carrying tourists from Moscow and St Petersburg, Ria Novosti reported.
The mountainous Kamchatka peninsula - more than 6,000 km (3,730 miles) east of Moscow - is popular among tourists.
The helicopter, manufactured during the Soviet era 37 years ago, was operated by Vityaz-Aero, a local private carrier. Its director said it had recently undergone maintenance and was in good shape.
The Mi-8 is a two-engine helicopter designed in the 1960s. It has been used widely in Russia, ex-Soviet countries and many other nations.
The area where the crash occurred can only be reached by helicopters, and fog complicated rescue efforts, the RIA Novosti reported. A total of 15 rescuers, including six divers, were involved in the rescue operation, according to Interfax.
Kamchatka, the pristine peninsula which is home to numerous volcanoes, is known for its rugged beauty and rich wildlife. The Kronotsky reserve, which has Russia’s only geyser basin, is a major tourist attraction on Kamchatka and helicopters regularly carry tourists there.
Quickly changing weather often makes flights risky. Last month, an An-26 passenger plane crashed on Kamchatka while approaching an airport in bad weather, killing all 28 people on board.
Russian news reports said Vityaz-Aero is half-owned by Igor Redkin, a millionaire businessman who is a member of the Kamchatka regional legislature. Redkin was placed under house arrest earlier this week after he shot and killed a man who was rummaging in a garbage bin. Redkin said the shooting was accidental after he mistook the victim for a bear.
There are an estimated 20,000 bears on Kamchatka, and they occasionally roam into settlements looking for food.