Ukrainian utility Ukrenergo said worsening winter frost would compound the situation after power plants were knocked out by the shelling.
Russia's Defence Ministry claimed responsibility for a “massive attack on Ukrainian military command systems and related defence, communications, energy and military facilities”.
The missile strikes came at a time when Ukraine was poised to switch from emergency to controlled power cuts, after few unscheduled shutdowns were needed at the weekend.
Thousands of engineers have worked to repair the damage to infrastructure caused by the Russian attacks, which have ramped up since October.
“The time that the Russians chose for this attack was connected with their desire to inflict as much damage as possible,” Ukrenergo boss Volodymyr Kudrytskyi told local television.
He said the attacks were launched as Ukraine entered a period of “peak frost”.
Mr Zelenskyy said most Russian missiles had been shot down with the help of western air defence systems.
“But, unfortunately, we still cannot ensure complete security to our sky — there were several hits,” he said during a nightly address that revealed the death of four people.
Ukraine conflict — in pictures
Western powers have said for months that Russia does not have enough missiles to maintain a constant barrage of attacks.
The latest onslaught came two weeks after the last and coincided with the start of a partial European oil embargo against Russia.
The Kremlin said it would not be deterred by an oil price cap introduced by G7 powers, Australia and the EU. The measure is meant to reduce Russian revenue.
Meanwhile, Moscow blamed Ukrainian drones for two explosions at airbases deep within its territory.
The bases in Russia's Saratov and Ryazan regions house nuclear-capable strategic bombers and are 500km from the Ukrainian border.
Two aircraft were damaged and three people killed when the drones crashed after being intercepted by air defences, Russian officials said.
Ukraine has not acknowledged responsibility for what would be its deepest strikes inside Russia since the war began.
“The sites are much deeper inside Russia than previous similar explosions,” Britain's Defence Ministry said in a daily intelligence update.
“If Russia assesses the incidents were deliberate attacks, it will probably consider them as some of the most strategically significant failures of force protection since its invasion of Ukraine.”