The plaintiffs, aged between six and 16 at the time of the disaster, say they got cancer from radiation exposure.
All of them underwent surgery to remove parts or all of their thyroid glands, their lawyer said.
However, they may struggle to prove that the radiation led to their cancer.
Their lawsuit is seeking $5.4m (£4m) in compensation from the plant operator Tokyo Electric Power Company (Tepco).
A Tepco spokesman said the company was aware of the case filing and would address it once they had seen the details of the complaint.