Officials of Tokyo Electric Power Company say workers found a leak from piping connecting two tanks around noon on Thursday.
The officials say a drop of water was leaking from a valve every few seconds. They found what looked like a crack in it.
The tanks hold contaminated water that was used to cool melted nuclear fuel. Cesium had been removed from the water.
The officials say the piping was covered with sheets as an emergency measure. The water in the two tanks is being transferred to other tanks.
The officials say there is no danger of the water seeping into the ground or out to other areas. That's because the storage tanks are surrounded by concrete barriers about 60 centimeters high, and the floors within the barriers are covered with resin.
The utility is stepping up efforts to prevent leaks following a series of similar incidents. About 300 tons of highly radioactive water leaked from a tank in August last year.
The firm is increasing patrols and installing water gauges and alarms to tanks.