The rabbit, caught on video which has since been posted on YouTube, also shows signs of albinism, a genetic mutation.
Meanwhile, Japan has announced that children in Fukushima city are to wear the radiation measuring devices, called dosimeters, in an attempt to calm public fears over radiation exposure.
Fukushima city is outside the Japanese government’s 12-mile no-go zone around the nuclear plant, but the plant is less than 40 miles away from the city and many residents are worried about radiation exposure.
And Greenpeace has urged Japan to evacuate pregnant women and children from Fukushima because of high radiation.
Residents were now being exposed to 10 to 20 millisieverts per year through the air alone, not counting contaminants inhaled or ingested through dust, water or food, Greenpeace said.
The rabbit was born on May 7 in the town of Namie just outside the 18-mile exclusion zone that has been imposed around the crippled plant, The Telegraph reports.
Namie has been identified as a radiation hot-spot.
According to reports, the rabbit also appears to have clear signs of albinism — a pure white coat and red eyes — the result of mutations in several genes.
Its owner, Yuko Sugimoto, said she had since stopped eating locally grown produce.