The researchers say it has nothing to do with the nuclear accident, and the child must have developed the thyroid cancer before the accident.
From Kyodo News (9/11/2012):
One case of thyroid cancer, under 18, according to the health survey of 80,000
The committee for "Fukushima Health Management Survey" to study the effect of radiation from the Fukushima I Nuclear Power Plant accident (headed by Shunichi Yamashita, Vice President of Fukushima Medical University) held a meeting on September 11, and it was reported that one case of thyroid cancer had been found among the subjects of the thyroid testing who were 18 years old and younger at the time of the accident.
About 360,000 [children] are scheduled to have thyroid examinations. So far, 80,000 children have been examined and the results are in.
Professor Shinichi Suzuki of Fukushima Medical University, which is in charge of the examinations, denied the effect of radiation exposure, saying in the committee meeting, "It took the minimum 4 years after the Chernobyl nuclear accident that a first case of thyroid cancer was reported. In Fukushima, there has been no external radiation exposure like in Hiroshima and Nagasaki, and no internal radiation exposure like in Chernobyl."
It's either Kyodo News misquoted Professor Suzuki or Professor Suzuki misrepresented the fact that 4 years after the Chernobyl accident the cases of thyroid cancer started to increase.
As to the supposed absence of internal radiation exposure, Professor Suzuki had better ask people like Mayor Abe of Kawasaki City (who's intent on force-feeding children with cesium oranges) or the Board of Education of Koriyama City (who wants to teach children about global warming by making them suffer through summer heat and radiation).
According to the latest data from Fukushima Prefecture, the examinations done in the fiscal 2012 (that started on April 1, 2012) so far are for children in Fukushima City (from May to August). Other major cities in Nakadori (middle third) are scheduled for later in the year, starting with Nihonmatsu City and Motomiya City in September. Testing in Koriyama City starts in October.
Compared to the results in the fiscal 2011 (that ended on March 31, 2012), the percentage of children with nodules or cysts of any size are larger in Fukushima City at 43.7%, compared to 35.8% in the fiscal 2011 results. Whether that means anything seems to depend on who you ask.
(Label translation is mine. The original document by Fukushima Prefecture is in Japanese only.)
All I know so far is that before the Fukushima nuclear accident, there were no routine thyroid checks for children; for that matter, there were none for adults either, unless thyroid problems were suspected by the doctors from other symptoms. In other words, there is no baseline data.
In the absence of the baseline data, there are some fantastic stories circulating on Twitter and blogs in Japan. Here's a togetter talking about: "According to my doctor, 40% of children tested in Kanagawa Prefecture were found with cysts on their thyroids!" and "I heard 40% of children tested in Kagoshima Prefecture had cysts!" The natural conclusion among people who were tweeting this horrible news is that the entire Japan is so contaminated that children are developing thyroid "abnormalities" everywhere in Japan.
A more logical conclusion (since Kagoshima is not contaminated with radioactive materials of Fukushima origin) is that maybe it is quite normal for about 40% of children at any location at any time to have small growths on their thyroids. But Japan has long ceased to be logical.
Someone even created an official-looking document saying "We were told that only Fukushima Medical University is allowed to conduct the thyroid test", and it was widely disseminated on the net. A day later, the document was yanked by the person who had posted it originally. Oh well. What can you believe these days?