Tokyo Electric Power (TEPCO), said one of its workers spotted drips coming from a tank used to store radioactive water at the site on Japan's tsunami-wrecked coast.
Water was leaking at the rate of one drop every three or four seconds, the company said, adding that absorbent material had been placed under the leak and workers were trying to stem the flow.
An increasing volume of water made radioactive after being used to cool the melted cores of broken reactors has become a growing headache for TEPCO, which has hundreds of tanks on the site.
Critics say improvised fixes put in place at Fukushima since the disaster leave it vulnerable to mishaps and at the mercy of nature.
Underwater storage pools have previously sprung leaks and a rat knocked out electricity supplies to cooling systems after it found its way onto a circuit board earlier this year.
On Monday TEPCO announced it had detected radioactive cesium in groundwater samples taken from the site, reversing an earlier announcement that the water was harmless.
The company had been intending to release the groundwater into the sea but suspended the plan in the face of strong protest from local fishermen.
Although the natural disaster that sparked the meltdowns claimed more than 18,000 lives, no one is officially recorded as having died as a direct result of the nuclear catastrophe.
However, tens of thousands of people were forced to leave their homes and businesses in the area around the site and many remain evacuated, with scientists warning some places may have to be abandoned forever.