Fighting on January 2 damaged the last remaining 330-kilovolt emergency power line supplying the plant, Grossi said in Vienna on Friday.
As a result, the Russian-occupied nuclear facility in southern Ukraine is ]relying solely on its main 750-kilovolt power line.
Grossi said a ceasefire would be needed within a roughly 10km radius of the plant to enable Ukrainian technicians to carry out the repairs.
The IAEA has already negotiated three such ceasefires in recent months, he added.
The plant's six reactors - the largest nuclear power facility in Europe - are shut down but must continue to be cooled.
IAEA observers have reported an increase in fighting near the site in recent weeks, Grossi said.
Ukrainian officials said on Friday that Russia attacked two foreign-flagged civilian vessels with drones in the southern Odesa region, killing a Syrian citizen and injuring another.
Russian forces have stepped up attacks on Ukraine's maritime export arteries over the last two months as retaliation for attacks on "shadow fleet" tankers heading to Russia to export its oil.
Ukrainian Deputy Prime Minister Oleksiy Kuleba said in a statement that one ship had been sailing along Ukraine's maritime export corridor to pick up a grain cargo at the port of Chornomorsk, and was under the flag of Saint Kitts and Nevis.
The other, near the Odesa port, was under the flag of the Comoros Islands and was carrying soybeans.
The deep-water seaports in Odesa region are crucial for Ukraine's commodity-heavy economy to export its products.
"This is yet another indication that Russia is deliberately targeting civilian objects, international shipping and food logistics," Kuleba wrote.
He posted images that showed ships bearing the names Ladonna and Wael K on their hulls.
According to MarineTraffic, a ship tracking website, the Ladonna is a 157-metre Comoros-flagged bulk carrier and the Wael K is a 115-metre general cargo ship.
Ukraine's seaport authority told Reuters on Wednesday that the number of Russian attacks on ports in the Odesa region had almost tripled from the previous year to 96 in 2025.
Meanwhile, Kyiv mayor Vitali Klitschko urged residents to leave the city of three million inhabitants temporarily, noting that 6000 apartment blocks could no longer be heated following Russian attacks.
"The city services are operating in emergency mode," Klitschko posted on Telegram.
About half the city's apartment blocks are affected following a severe Russian air attack on the Ukrainian capital.
The overnight attack on Kyiv had been the most serious of the war for the city's infrastructure, with the situation exacerbated by cold winter weather, Klitschko said.
Those able to find suitable accommodation elsewhere should leave the city temporarily, he said.
The recommendation was not an official order to leave but advice to the effect that residents should travel to their dachas equipped with heating stoves or seek accommodation with friends and relatives in less affected areas.
Some of the apartment blocks should have heating again from Friday evening, Klitschko said, adding that the situation in Kyiv was difficult but under control.
The Energy Ministry said on Friday morning about 500,000 consumers were without electric power in Kyiv and surroundings.
The Ukrainian air force said the city had come under overnight attack from more than 200 drones and dozens of missiles and cruise missiles.
At least four people died in the attacks, and President Volodymyr Zelenskiy said that 20 apartment blocks had been damaged.
Zelenskiy said the strike was "demonstratively" close to Ukraine's border with European Union countries.
He said the Oreshnik medium-range ballistic missile used by Russia also posed a challenge to countries such as Poland, Romania and Hungary, among other EU members.
with DPA