The incident is the worst since last August, when a series of similar leaks sparked international alarm.
Tokyo Electric Power Co (Tepco) said the latest leak was unlikely to have reached the ocean.
However, news of the leak at the site, which was devastated by the 2011 earthquake and tsunami, is likely to further erode public trust in a utility which has been rocked by a string of mishaps and official criticism of its clean-up operation.
Masayuki Ono, a spokesman for Tepco, said: "We are taking various measures, but we apologise for worrying the public with such a leak."
The firm said water overflowed from a storage tank at the site late on Wednesday after a valve had been left open by mistake and sent too much contaminated water into a separate holding area.
A worker patrolling the area, around 700 yards from the ocean, spotted water leaking through a drain attached to the side of the tank.