Cases included fires, water and oil leaks at the plant triggered by Monday's magnitude-6.6 quake, and pipes knocked out of place, Kyodo News agency reported, quoting the plant operator, Tokyo Electric Power Co.
TEPCO officials could not immediately confirm the report.
The Kariwa nuclear power plant at Kashiwazaki city, near the epicenter, is the world's largest in terms of power output capacity.
With nine people dead, over a thousand others injured, hundreds of collapsed buildings and damaged roads and train tracks, Japan got a new jolt from Monday's quake as officials who first said the nuclear power plant had no radioactive leak admitted 12 hours later that it did.
About 100 drums containing low-level nuclear waste fell over at the plant during Monday's 6.8-magnitude quake and were found a day later, some with their lids open, said Masahide Ichikawa, an official with the local government in Niigata prefecture.
The power company is working to determine whether any hazardous material had spilled, said Ichikawa, citing a report by the company.
With highways ripped up and bridges destroyed, officials struggled to get emergency supplies to the quake region, where nearly 13,000 people have crowded into evacuation centers amid worries of mudslides and more aftershocks.
Some 53,000 homes in the quake zone are without water, 35,000 are without gas as of early Tuesday, and over 25,000 households are without power.
Further complicating the cleanup during what is Japan's rainy season, forecasters are predicting heavy rain, flooding and lightning in the area.
Chief Cabinet Secretary Yasuhisa Shiozaki said Tuesday that officials are still assessing the damage. "The most important thing is to take necessary measures quickly and respond to the needs of the victims," he said.
Many of the injured suffered broken bones, cuts and bruises. "I got so dizzy that I could barely stand up," said Kazuaki Kitagami, a worker at a 7-Eleven convenience store in Kashiwazaki, the hardest-hit city. "The jolt came violently from just below the ground."
The Japanese Meteorological Agency put the magnitude at 6.8, while the U.S. Geological Survey said it was 6.6.
In Kashiwazaki, the quake reduced older buildings to piles of lumber. On Tuesday morning, officials said a total of 342 houses had been destroyed and another 469 were damaged.