The nuclear power plant, located on the Dnipro River in southern Ukraine, was taken over by Russian forces in March.
It is the largest of its kind in Europe, with six reactors.
The plant was targeted by shelling on Friday. Russia and Ukraine accused each other of carrying out the attack.
Rafael Mariano Grossi, head of the International Atomic Energy Agency (IAEA), has said in a statement: “I’m extremely concerned by the shelling yesterday at Europe’s largest nuclear power plant, which underlines the very real risk of a nuclear disaster that could threaten public health and the environment in Ukraine and beyond.”
Mr Grossi, who leads the United Nation’s nuclear watchdog, urged all sides in the Ukraine conflict to exercise the “utmost restraint” around the plant.
He said military action jeopardising the safety and security of the Zaporizhzhia plant “is completely unacceptable and must be avoided at all costs”.
The IAEA chief added: “Any military firepower directed at or from the facility would amount to playing with fire, with potentially catastrophic consequences.”
Shells hit a high-voltage power line at the plant, prompting its operators to disconnect a reactor despite no radioactive leak being detected.
Even though the plant was captured by Russian forces in the opening phase of the war, it is still run by its Ukrainian technicians.
Ukraine’s state nuclear power company Energoatom blamed Russia for the damage at the power station but Russia’s defence ministry accused Ukrainian forces of shelling the plant, saying a leak of radiation had been avoided only by luck.
Ukrainian President Volodymyr Zelensky said Russia was responsible and accused it of committing “an open, brazen crime, an act of terror”. He called for sanctions on the entire Russian nuclear industry.
Earlier this week, the UN’s nuclear watchdog appealed for access to the plant, which Washington claims Moscow is using as a battlefield shield.
The plant is about 160 miles (200km) northwest of the Russian-held port of Mariupol in southeast Ukraine.
Further east of the city, Kyiv and Moscow have both claimed small advances. Russian artillery has bombarded towns and villages across a wide area in a now-familiar tactic.
Kharkiv, Ukraine’s second city, was subjected to renewed shelling early yesterday (August 5). Kharkiv Mayor Ihor Terehov said on Telegram: “All of Kharkiv heard the sounds. The rescue teams are on site.”
The southern city of Mykolaiv was shelled last night with one person killed, Mayor Oleksandr Senkevych said on Telegram. He said 22 people were injured with 21 private homes and five residential buildings damaged.
The UN’s atomic watchdog announced in June it had lost connection again to its surveillance systems which keep track of nuclear material at the Zaporizhzhia nuclear power plant.
It was the second time during the month. Ukraine’s nuclear power operator said days later it had re-established its connection.
Energoatom said at the time the link had been lost due to the cutting off by “the occupiers” of all Ukrainian mobile operators, including Vodavone, with which the IAEA has a contract for data transmission.
The IAEA said in July the incident underscored the urgent need to dispatch a mission to the plant.