Jason Makula claims he suffered "great physical pain, mental anguish and bodily injuries" after a temporary wall fell on him at the New York venue where NTS staged Alan Cumming's one-man Macbeth.
Shakespeare's "Scottish play" is infamous for the disasters that have befallen productions since it was first performed in 1606.
Makula claims the injuries led to large medical bills, and have left him facing "continuous pain and suffering in the future" and are hampering his ability to work. He says NTS fell short of required safety standards by failing to use proper equipment to remove the stage wall at the end of the play's run last July at the Jazz At Lincoln Centre, where he worked.
As NTS was in charge of the venue at the time, they were "absolutely liable", Makula claims.
Makula, thought to be in his early 40s, is demanding a jury hearing. Both sides are due to appear before a judge in a pretrial conference on May 20. If no settlement is reached, the case should come to trial within 45 days. It is understood Makula is separately suing the venue.
The lawsuit has cast a shadow over one of NTS's most successful US outings. Set in a mental hospital, with Scots-born Cumming playing all the key roles, the production is now winning rave reviews on Broadway.
NTS, which had an income of £6m last year, is vigorously defending the damages lawsuit. Its New York lawyers accept Makula was injured, but deny NTS was at fault. They suggest either Makula or his immediate colleagues were to blame.
It is understood union rules barred NTS staff from helping directly in the dismantling of the set, and NTS workers watched helplessly from a distance as the accident took place.
Court papers obtained by the Sunday Herald show Makula's lawyers, personal injury specialists Harris/Law, filed an action at New York Supreme Court in October, initially against NTS and its US offshoot, NTS America Inc.
The complaint said NTS had a duty to keep the venue safe but had allowed it to be "in an unsafe, defective, hazardous and/or dangerous condition". It further claimed NTS had failed to secure a temporary wall for removal, failed to use proper equipment, and failed to warn Makula and others of the hazard, so that on July 15, Makula was "caused to fall with great force and violence".
The event was "caused wholly and solely by reason of the carelessness, recklessness and negligence" of the NTS, its agents or employees, Makula's complaint alleges.
NTS's US lawyers replied with a denial of responsibility in mid-January. It was not until late February that Makula's side put a figure on the damages. "At the present time plaintiff demands twenty million dollars ($20,000,000)," it said.
The firm also revealed Makula, of New Haven, Connecticut, had run up bills with the Beth Israel Hospital in New York, as well as eight other medical providers.
Last month the case was dropped against NTS America Inc, leaving the NTS in Glasgow as sole defendant, and the action was transferred from the Supreme Court to New York Southern District Court.
Harris/Law describes itself as New York's Premier Personal Injury Law Firm, and says it has a "proven record of getting the largest cash awards for victims and their families in the least amount of time".
Although Makula has asked for $20m, none of the case histories on the Harris/Law website mentions damages above $10m. The firm's founder and chairman, Steven R Harris, declined to comment.
NTS has toured the US with acclaimed productions including Black Watch and The Strange Undoing Of Prudencia Hart. The Scottish Government funded 75% of its income last year.
A spokeswoman said: "The National Theatre of Scotland vigorously denies any liability in this matter."
Macbeth has a long history of disasters. An 1849 performance in New York ended in a riot that left more than 20 people dead.