Hydrochloric acid, used to neutralise alkaline water being decontaminated, was found seeping from a pipe joint, Tokyo Electric Power Co (TEPCO) said in a statement.
The joint was wrapped in a vinyl bag to contain the leakage, TEPCO said, adding it was investigating the cause of the trouble.
About one litre of hydrochloric acid has been contained in the bag.
The leak was found at one of three Advanced Liquid Processing System units designed to remove radioactivity from contaminated water at the plant, where a massive earthquake and tsunami in March 2011 sent nuclear reactors into meltdown.
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The troubled system was one of two units that had been in trial operation and were scheduled to go into full operation today.
In late September plastic padding clogged up a drain in the same system, causing it to shut down. In October, it was halted due to a programming mistake.
Thousands of tonnes of water, used since the meltdown to cool reactors or polluted by other radioactive material, are being stored in huge tanks at the site on Japan's northeast coast.