A general view of the Zaporizhzhia Nuclear Power Station in territory under Russian military control, southeastern Ukraine. AP
Zaporizhzhia is the biggest nuclear power plant in Ukraine and in Europe.
The plant has been under Russian control since March, and Ukraine has accused Moscow of basing hundreds of soldiers and storing arms there.
"Limit your presence on the streets of Energodar! We have received information about new provocations by the (Russian) occupiers," Ukraine's nuclear agency Energoatom said as it shared a message on Telegram from a local chief in Energodar city, where the plant is located.
The city remains loyal to Kyiv.
"According to residents, there is new shelling in the direction of the nuclear plant... the time between the start and arrival of the shelling is 3-5 seconds," the message said.
But pro-Moscow officials in the occupied areas in Zaporizhzhia region blamed Ukrainian forces for the shelling.
"Energodar and the Zaporizhzhia nuclear plant are again under fire by (Ukrainian President Volodymyr) Zelensky's militants," said Vladimir Rogov, a member of the Moscow-installed administration.
The missiles fell "in the areas located on the banks of the Dnipro river and in the plant", he said, without reporting any casualties or damage.
Areas occupied by Russia and those under Ukraine's control are divided by the Dnipro river.
Kyiv and Moscow have traded accusations over several rounds of shelling on the plant this month, raising fears of a nuclear catastrophe and led to an emergency meeting of the UN Security Council on Thursday.
Ukraine said the first strikes on August 5 damaged a power cable and forced one of the reactors to stop working.
Then strikes on Thursday damaged a pumping station and radiation sensors.
Ukraine, backed by Western allies, has called for a demilitarised zone around the plant and for the withdrawal of Russian forces.