In total, around 120 missiles and 90 drones were launched, Mr Zelensky said on Telegram.
Ukraine’s largest private energy company, DTEK, said the latest Russian attacks caused “significant damage” to its thermal energy plants.
It was the eighth large-scale attack on its energy facilities this year, the company said in a statement, adding that its plants had been targeted more than 190 times since the start of Russia’s full-scale invasion in February 2022.
Ukrainian officials fear it could signal another concerted Russian attempt to deplete the power grid as winter arrives.
In Ukraine’s south, the city of Mykolaiv was among the worst hit, with at least two people killed and several injured, while the Black Sea port of Odesa experienced a city-wide power cut.
In the capital, Kyiv, fragments from intercepted missiles and drones fell in several places, but there were no reports of injuries.
Poland, Ukraine’s neighbour to the west, scrambled fighter jets to patrol its own airspace as a security precaution, Poland’s Operational Command said.
“Due to a massive attack by Russia, which is carrying out strikes using cruise missiles, ballistic missiles and drones against sites located, among other places, in western Ukraine, operations by Polish and allied aircraft have begun,” it said.
Last weekend, Russia and Ukraine both exchanged blows in series of drone raids which were the largest attacks of that type against each other since the start of the war.
Russia’s defence ministry said it intercepted 84 Ukrainian drones over six regions, including some approaching Moscow, which forced flights to be diverted from three of the capital’s major airports.
Ukraine’s air force said Russia launched 145 drones towards every part of the country on 9 November, with most shot down.