The power plant has six Russian-designed reactors. It was first commissioned in 1984, two years before the Chernobyl disaster, and has since been expanded and upgraded.
The plant is situated in Enerhodar, a city on the banks of the Dnieper River, a few hundred kilometers from the Black Sea in south-eastern Ukraine.
Russia has already captured the defunct Chernobyl plant, about 100 kilometers north of Kyiv, which spewed radioactive waste over much of Europe when it melted down.
The Zaporizhzhia reactors are of a different and safer type, analysts said.
What’s the latest?
Russian troops have been attacking Enerhodar as part of a drive to cut the rest of Ukraine off from the sea.
Local emergency services said Russian shelling caused a fire in one of the plant’s training buildings, but said they extinguished it on Friday morning.
Soon after the fire was put out the regional military administration said Russian forces had taken control of the site.
The military released a statement saying Russian attacks had caused some damage to the compartment of the plant’s number 1 reactor, but had not affected its safety.