Electricity supplies from other plants were being routed to areas normally serviced by the station, Sergei Shoigu, the emergency situations minister, said.
"There is no threat to villages downstream from the Sayano-Shushenskaya hydroelectric power station," Shoigu said. "There is no threat of damage to the dam."
Power shortages have been reported in the city of Tomsk and the mining area of Kuzbass, the RIA Novosti news agency said.
Andrei Klyuyev, an emergency situations ministry official at the site of the accident, 4,000km east of Moscow, said there were still dozens of people unaccounted for.
Klyuyev said rescue divers had pulled out one person from a room underneath the plant's turbine hall where there was apparently a cave-in and flooding but said many more could still be trapped.
Russian television broadcast pictures showing pieces of concrete, cables and twisted metal pylons beneath the dam wall and the main turbine hall flooded with water and debris.
The natural resources ministry said it was concerned by the environmental impact of the accident, saying an oil slick of more than 25km had spread along the Yenisei River.
"According to preliminary data, transformer fluid has leaked from one of the hydroelectric station's damaged units," the ministry said in a statement.
Analysts have warned that Russia needs to boost its power production significantly to meet the growing demand of industrial producers or it will face regular power shortages.
The country's ageing infrastructure has long been regarded as a key obstacle to Russia's development.