Drones attacked the plant, Europe's biggest, on Sunday, hitting one reactor building, the International Atomic Energy Agency has said, adding that nuclear safety was unaffected.
Russia and Ukraine have repeatedly accused one another of targeting Zaporizhzhia; both sides deny doing so.
Russia's Ambassador to the IAEA Mikhail Ulyanov said on Monday evening that his country had called an emergency Board meeting "with regard to the recent attacks and provocations of the armed forces of Ukraine against the #ZNPP".
The IAEA has yet to announce a meeting date. The Board's rules state that any country on it, including Russia, can call a meeting. Wednesday is a holiday at the United Nations in Vienna for the Muslim feast of Eid al-Fitr marking the end of Ramadan.
The Board is the IAEA's top decision-making body that meets more than once a year. Russia is likely to again blame Ukraine for the recent drone strikes at Zaporizhzhia but it is unlikely to receive broad backing from the Board, which last month passed a resolution calling on Russia to withdraw from the plant.
The IAEA has not assigned blame for the attacks but demanded that they stop.
"Such reckless attacks significantly increase the risk of a major nuclear accident and must cease immediately," IAEA chief Rafael Grossi said on Sunday.
(Reporting by Francois Murphy; Editing by Andrew Heavens and Philippa Fletcher)
