The water came from one of the seven underground reservoir tanks storing water for cooling Fukushima's reactors, the Tokyo Electric Power Co. (TEPCO) said in a statement.
TEPCO did not say what caused the leak or when did it appear, but said it assumed "that there is no leakage to the ocean since there is no drainage ditch near the reservoir".
The tank is located abtout 800 metres from the sea.
The whole amount of radioactivity in the leaked water is estimated at about 710 gigabecquerel, the company said.
TEPCO is pumping the remaining 13,000 tonnes of water from the leaked tank to another reservoir, though the process may take up to five or six days.
The company earlier reported that a cooling system of the Unit Three spent atomic fuel storage facility temporarily failed Friday, but the problem was fixed in about three hours.
Three similar incidents were reported at spent fuel facilities at the plant's units One, Three and Four last month.
In March 2011, Japan was hit by a massive 9.0-magnitude quake which caused a tsunami, claiming over 15,000 lives and triggering a number of explosions at the Fukushima plant.
The tsunami caused a partial meltdown at three of the plant's reactors. Radiation leaked into the atmosphere, soil and seawater, making the accident the world's worst nuclear disaster after Chernobyl.
Japan will need at least 40 years to recover fully from the nuclear catastrophe, scientists say.
Some 315,000 victims are still living in a temporary housing unable to return to their houses in the plant's vicinity.
Fukushima's cooling systems sustained a one-day power outage in late March. The incident was tentatively blamed on a rat that short-circuited the switchboard with its body.