A local official said the magnitude 6.8 quake on Monday tipped over some 100 steel barrels sealed to store radioactivity-contaminated gloves and clothes within the plant.
"This may cause people to distrust nuclear power."
Shoji Iida, a spokesman for Kariwa village where the nuclear facility is located, said they did not know exactly how many containers were found open.
He said 800 litres of oil also spilled inside the facility, but there was no radiation risk.
Kensuke Takeuchi, a spokesman at the nuclear plant, confirmed that barrels of low-level nuclear waste had tipped over but did not give further details.
"We're currently investigating the situation and plan to deal with it as smoothly as possible," Takeuchi said, while refusing to offer further comment.
Another spokesman, Manabu Takeyama, said "at this point in time, there is no danger of grave effects on the environment or human health from the plant".
School gymnasiums have been turned into evacuation
centres to house quake victims [EPA]
Late on Monday, Tokyo Electric admitted that water containing a "small amount of radioactive material" had leaked from its nuclear plant near the quake epicentre, but downplayed the potential danger.
Following the incident, Japanese officials on Tuesday called for a review of safeguards at the reactor where a fire blazed for hours spewing thick black smoke out of the electricity-supplying part of the facility.
Akira Amari, Japan's economy, trade and industry minister, warned Tokyo Electric on Tuesday over the delay in putting out the fire.
"This may cause people to distrust nuclear power," Amari said. "We will not have the plant resume operations without confirming safety."
Tsunehisa Katsumata, the company president, admitted that there was "weakness in our extinguishing measures".
Japan, which has few natural energy resources of its own, relies on nuclear power for nearly 35 per cent of its needs, the second highest figure after France.
Meanwhile, thousands of people have fled their homes in Japan's northwest coast amid fears of mudslides and aftershocks following a powerful earthquake which killed nine people.
School gymnasiums and community halls have been converted into evacuation centres to house victims of Monday's quake.
Japanese officials said more than 1,000 people suffered light injuries and one person was still missing.
The magnitude-6.8 quake off the coast of Niigata prefecture toppled hundreds of buildings and disrupted transportation.
Yasuhisa Shiozaki, the chief cabinet secretary, said the assessment of damage, more severe than expected, was still going on.
More than 1,000 policemen and firefighters have been sifting through heaps of debris from destroyed houses searching for survivors.
Japan's defence ministry dispatched 450 troops and seven battleships early on Tuesday to support rescue operations in the region, which has been hit by nearly 100 aftershocks.
Japan lies at the junction of four tectonic plates and is hit by about 20 per cent of the world's most powerful earthquakes.