More than 50 missiles and 20 drones were used in the attack, he wrote in a post on X, formerly known as Twitter.
It marks the latest in a string of Russian attacks on Ukraine's energy grid, which Moscow insists is a legitimate military target.
The strikes targeted seven regions across the country and took place on a major national holiday commemorating the defeat of Nazi Germany in World War Two.
Writing on social media, Mr Zelensky drew parallels between the German invasion of the Soviet Union and the Russian invasion of Ukraine, referring to Russian President Vladimir Putin's regime as "Moscow Nazis".
The energy provider said its teams were on site and working to restore power, although 80% of its generating capacity had already been damaged or destroyed.
"The energy these power stations produce allow millions of Ukrainians to live with dignity," said Chief Executive Maxim Timchenko. "We will not stop working to restore power at our facilities."
Ukraine's energy ministry said that there "may be limitations to energy supply" for industrial consumers between 18:00 (16:00 BST) and 23:00 as a result of the damage.
The strikes focused on key energy and transport sites in Kyiv, Vinnytsia, Poltava, Kirovohrad, Zaporizhzhia, Ivano-Frankivsk and Lviv, Ukrainian officials said, adding that Soviet-era powerplants and gas storage facilities were among the targets.
"The enemy has not abandoned plans to deprive Ukrainians of light," said Energy Minister Herman Halushchenko.
Interior Minister Ihor Klymenko said two people in Kyiv were injured in the attacks, while one child in the Kirovhrad region was also hurt.
In Kharkiv, two other children were hurt according to Oleg Sinegubov, the head of the region's administration.
Despite the damage, Ukraine's air force said it intercepted dozens of missiles and 20 of 21 Iranian-made Shahed drones fired towards the country.
Russia's defence ministry says it used high-precision Kinzhal hypersonic missiles.
Experts say the true impact of the Russian attacks may not be felt until annual energy consumption peaks in the winter.
Last month, a powerplant near Kyiv was destroyed that provided electricity for three regions.
Ukrainian forces targeted an oil storage depot near the Russian-occupied city of Luhansk in eastern Ukraine on Tuesday night. Russian-appointed officials in the area said five workers were hurt.
Meanwhile, border officials in Poland said they had detained a deserter from the Russian military as he crossed into the country from Belarus.
Authorities said the 41-year-old man would face further action in the coming days. Polish radio reported that he was dressed in civilian clothes and was unarmed when detained.
The outlet added that he had been carrying Russian military papers when arrested.
Russia's defence ministry said its attacks were in response to Ukrainian strikes on their energy facilities. While Ukraine has targeted several Russian oil facilities in recent weeks, Russia has bombarded Ukrainian power plants ever since the start of winter in 2022.
The latest Russian campaign targeting Ukraine's energy grid began in March. Waves of attacks have forced authorities in Ukraine to impose rolling blackouts in several regions.
On Tuesday Mr Putin was sworn in for his fifth term as president and said Russia would emerge through a "difficult pivotal period" even stronger.
President Zelensky accused Russia of "demonstrating that Nazism has resurfaced with each new crime".
"This time, it simply has a new label: 'Made in Russia.'"
According to Ukraine's largest energy provider, DTEK, at least three thermal powerplants were seriously damaged in Wednesday's attack, the fifth on the company's facilities in seven weeks.
ReutersRussia has launched a "massive" early morning missile and drone attack on energy facilities across Ukraine, President Volodymyr Zelensky has said