A fire also broke out at the station.
Russian troops are now in control of Europe's largest nuclear power station, according to Ukrainian officials.
Shelling overnight caused a fire to break out at the Zaporizhzhia plant.
The blaze was extinguished and radiation levels are said to be normal.
The UK Ministry of Defence says the port city of Mariupol "remains under Ukrainian control but has likely been encircled by Russian forces".
The city, on the Black Sea, has been "subjected to intense Russian strikes".
Both the US President and the British Prime Minster have spoken by telephone with the Ukrainian President Volodymyr Zelenskyy overnight, to get updates on the blaze.
Boris Johnson says the reckless actions of President Putin could now directly threaten the safety of all of Europe.
The US Energy department has activated its nuclear incident response team as a precaution.
Ukraine's president says "only urgent action by Europe" will stop the Russian invasion.
Speaking overnight, Volodymyr Zelenskyy said he fears this is the catastrophe that could lead to the continent's "evacuation".
President Volodymyr Zelenskyy had this warning if nothing's done to help:
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