The International Atomic Energy Agency (IAEA) - the United Nations' nuclear watchdog - criticized and said that such attacks pose a great risk of causing disaster.
More than a dozen explosions rocked Europe's largest nuclear power plant on the evening of 19 and 20 November.
According to Reuters, Russia and Ukraine blamed each other for the shelling as they have blamed each other after the explosions in recent months.
IAEA Director General Rafael Grossi said that the news about the explosions was extremely worrying.
"The explosion at the site of Europe's largest nuclear power plant is completely unacceptable. Whoever was behind the incident must stop immediately. As I have said many times before, you are joking with the fire!" - Mr. Grossi said in a statement.
Citing information provided by the plant's management, the IAEA expert team at the site said that there were damage to several buildings, systems and equipment, but that no equipment was important for nuclear safety and security so far.
The IAEA experts plan to conduct an assessment today (November 21). However, Russian nuclear power operator Rosenergoatom stressed that there will be limitations in what the group can check.
"They explain their mission as unlimited. In reality, that is not the case. If they want to check a facility that has nothing to do with nuclear safety, they will be rejected," Renat Karchaa, adviser to Rosenergoatom, told TASS.
Consecutive shelling of the nuclear power plant in southern Ukraine has raised concerns about the possibility of a serious accident just 500km from the site of the world's worst Chernobyl nuclear disaster.
The Zaporizhzhia nuclear power plant supplied about a fifth of Ukraine's electricity output before Russia's military campaign and has been forced to operate many times with backup generators.
The plant has six water-cooled and water-regulated VVER-1000 V-320 reactors designed by the Soviet Union containing uranium 235.
Reactors have stopped working but there is a risk that nuclear fuel could overheat if the cooling system power source is cut off. The artillery has repeatedly cut off power lines.
IAEA Director General planning Zaporizhzhia Grossi plans to visit France's BFM plant and canal, the agency reported.
The Russian Defense Ministry accused Ukraine of bombing the plant's power lines. According to Renat Karchaa - advisor to the CEO of Rosenergoatom - some of the factory's storage facilities have been shelled by Ukraine. The firecrackers fell near a dry nuclear waste storage facility and a new nuclear fuel storage building, but no radioactive emissions have been reported.
Meanwhile, Ukrainian nuclear energy giant Energoatom accused the Russian military of dropping artillery at the site, with at least 12 shells hitting the plant's infrastructure.
Energoatom said that Russia has targeted facilities used to restart the plant's parts in an effort to further limit Ukraine's power supply.