The plant operated by the Kyushu Electric Power Co. reported to local authorities it was having a problem with a pump Friday, but didn't immediately disclose the leak, the Kyodo news agency reported.
Officials said the No. 3 reactor was shut down when temperatures rose and the water leaked. It was all contained and has since been recovered, they said.
Regardless, Genkai Mayor Hideo Kishimoto told reporters he was angry with the utility for withholding the information.
"It should have been reported properly," the mayor said.
The Nuclear and Industrial Safety Agency said the leak hadn't posed a safety threat, but ordered an investigation into the incident, the report said.
Elsewhere Friday, Prime Minister Yoshihiko Noda announced temperatures in three melted reactor cores at the tsunami-damaged Fukushima power plant had fallen below boiling, China's state-run Xinhua news agency reported.