In a statement posted on its website, Kansai Electric said it has found 34 litres of radioactive water at the No 4 unit at its Takahama nuclear plant in Fukui prefecture, 500 km (310 miles) west of Tokyo.
The water has been cleared and there has been no impact on the environment, the company said, adding that it is investigating the reasons for the leakage.
The statement did not say if the restart would be delayed and company officials could not immediately be reached for comment.
Kansai Electric shut down the reactor in July 2011, months after an earthquake and tsunami devastated the Fukushima nuclear power plant operated by Tokyo Electric Power Co Similar radioactive water leakages have also been found at the Fukushima.
Kansai Electric restarted its Takahama No 3 reactor late January as part of test operations, making it the third reactor in Japan to resume operations after passing stringent safety checks imposed following the Fukushima disaster.
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