Ye Meng Yuan was lying on the ground near the wreckage at San Francisco International Airport when she was run over by two fire vehicles.
According to the San Francisco Chronicle, the suit claims that rescue workers saw the girl lying on the ground but inexplicably failed to evaluate her condition, treat her, mark her location or remove her from harm's way.
The suit was filed in San Mateo County Superior Court on behalf of her parents in China.
It seeks unspecified damages.
A spokesperson for the city attorney's office said he had not seen the lawsuit and couldn't comment.