The Ukrainian nuclear company says fighting made it impossible to immediately repair the high-voltage power line to the plant, which was captured by Russian forces.
Energoatom said there were about 20,000 spent fuel assemblies at Chernobyl that could not be kept cool amid a power outage.
Their warming could lead to the release of radioactive substances into the environment, it said in a statement.
"The radioactive cloud could be carried by wind to other regions of Ukraine, Belarus, Russia, and Europe."
Without power, ventilation systems at the plant would also not be working, exposing staff to dangerous doses of radiation, Energoatom added.
On Tuesday, the UN nuclear watchdog warned the systems monitoring nuclear material at the radioactive waste facilities at Chernobyl had stopped transmitting data.
The still-radioactive site of the world's worst nuclear disaster lies some 100km from Kyiv.
Its fourth reactor exploded in April 1986 during a botched safety test, sending clouds of radiation billowing across much of Europe.
