The civil action was filed Thursday on behalf of the victim, whose arm was branded last spring using a heated metal coat hanger shaped into a swastika.
The lawsuit, seeking unspecified compensatory and punitive damages, alleges a McDonald's owner in Farmington hired employees in violation of corporate policies requiring a safe environment for customers.
A message left through McDonald's corporate media relations office was not immediately returned Friday.
Another defendant, McDonald's franchise owner John Bronson of Durango, Colo., didn't return a telephone message seeking comment.
Former McDonald's employees Paul Beebe, William Hatch and Jesse Sanford have pleaded not guilty to federal criminal charges. The three Farmington-area men are the first defendants in the nation to be prosecuted under a law that makes it easier for the government to bring charges against people accused of committing hate crimes.
The lawsuit was filed in state District Court in Santa Fe by Albuquerque attorney Ron Morgan on behalf of the victim's mother. Morgan said he pursued the action because of hardships to the victim and his family.
"It's what trial lawyers do when they see facts that indicate a lawsuit is appropriate," Morgan said. "The criminal system doesn't go after corporations."
The Associated Press is not identifying the woman or her son because authorities have said the victim's disability was a motive for the alleged hate crime. The lawsuit says he "has obvious child-level behaviors and diminished physical abilities" and cannot function as an adult.
The three McDonald's employees encountered the man when he came in for an evening meal on April 29. One of the workers took him to an apartment, where the other two later joined them.
The lawsuit says the men branded a swastika on the man's arm using a heated metal coat hanger, shaved a swastika on the back of his head and drew "satanic, sexual, hate-filled images and degrading words" on his body using a permanent marker, and filmed and photographed the episode.
According to the complaint, McDonald's corporate polices require background checks for job applicants to ensure the safety of children, the handicapped and the elderly. The lawsuit says the men were unfit to work in a McDonald's since each had "multiple criminal convictions including felonies and other anti-social history."
The lawsuit doesn't detail that alleged criminal history, but it says at least six employees at the Farmington restaurant had a criminal background, including the manager on duty on April 29.