The leak in a tunnel linked to the No 2 reactor has raised fears of radioactive liquid seeping into the environment.
Plutonium has also been found in soil at the plant, but not at levels that threaten human health, officials say.
Earlier, Japan's government strongly criticised the plant's operator, Tepco, over mistaken radiation readings.
Tepco announced on March 27 that a highly radioactive pool of water in the No 2 reactor was 100 times more radioactive than it actually was.
Up until now, pools of water with extremely high levels of radiation have only been detected within the reactor buildings themselves.
Radiation levels were measured at 1,000 millisieverts an hour, a dose that can cause temporary radiation sickness.
However, Tepco said there was no evidence that the contaminated water had reached the sea.
Plutonium was used in the fuel mix for only one of the six reactors, number three.
The twin discoveries came hours after the government criticised Tepco for issuing incorrect readings from the plant.
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