They removed the wrong pipe from equipment at the plant, sending toxic water spilling onto them and the entire floor of the facility housing a set of three units designed for primary, partial water treatment, a spokesman for Fukushima Dai-ichi nuclear plant operator Tokyo Electric Power Co (Tepco) said.
Exposure to the workers, who were wearing face masks with filters, protective hazmat suits and rain gear, is believed to be minor but is still under investigation. The six were part of an 11-member team and the remaining five were not affected.
The workers managed to reattach the pipe.
The accident is the latest in a spate of leaks and other problems caused by human error that have added to public criticism of Tepco's handling of the crisis at the plant, which is still in a precarious condition since the meltdowns following the March 2011 earthquake and tsunami.
Last week, workers overfilled a storage tank without fully checking water levels, causing a leak and in August a 300-ton leak seeped from another storage tank.
Japan's Nuclear Regulation Authority Chairman Shunichi Tanaka said: "Careless mistakes are often linked to (declining) morale."