External radiation levels were not affected, the company said.
The magnitude 7.6 quake, which killed more than 200 people in the Hokuriku region, shook the idled Shika power station, which is located around 65 kilometres (40 miles) from the quake's epicentre.
After a first oil leak detected on Sunday, a film of oil was detected on Wednesday in several gutters surrounding the main transformer of the No.2 reactor, the company said.
Also, an oil slick measuring about 100 meters by 30 meters was found floating on the sea in front of the power station, near the area where the first slick was observed.
Hokuriku Electric said it had placed oil absorption mats in the gutters and on oil fences in the coastal areas, and closed the drainage gate for rainwater after the latest leak.
The gate was opened on Tuesday because no additional oil was detected during monitoring patrols conducted three times a day.
"We regret that we should have been more careful in our decision," Masayuki Nunotani, general manager of Hokuriku Electric's nuclear energy division, told reporters.
The utility believes the second oil leak originated from a transformer during the Jan. 1 quake, but said it was still analysing further details.
Key external power supplies, monitoring facilities, and cooling systems at the plant are functioning normally, it said.
But at a regular meeting by the Nuclear Regulation Authority (NRA) on Wednesday, its secretariat reported that the acceleration of shaking observed at the Shika plant during the Jan. 1 quake slightly exceeded design assumptions in some parts, Kyodo news agency said.
The NRA said there is no safety problem, but a committee member stated that the magnitude of the earthquake was extremely large, and the results of the experts' research on the quake must be used in future examinations, Kyodo reported.
