The blaze has spread to about 250 acres, The Evening Standard newspaper on Sunday quoted Ukraine's state ecological inspection service Yehor Firsov as sayin.
The Emergency Services Ministry sent 130 firefighters and two planes to put out the fire.
It said radiation levels had increased at the fire's centre.
The blaze is within the 2,600-square kilometre Chernobyl Exclusion Zone established after the the world's worst nuclear disaster in April 1986 that took place when the plant's No. 4 reactor exploded.
The explosion sent a cloud of radioactive fallout over much of Europe, the newspaper report said.
The zone is largely unpopulated, although about 200 people have remained there despite orders to leave.
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