According to the New York Post, Australian actress Natalie Mendoza, 30, who plays Arachne, was hit on the head by equipment in the wings during the first preview and she suffered a concussion.
Feeling fine she decided to continue against her doctor's advice, but fell ill the next day.
Mendoza, who was once engaged to showman David Campbell, will now be out of the picture for at least a week, while understudy, America Olivo, a former Playbill cover model, will take over the role.
The show, which is due to open January 11, saw Kevin Aubin, an aerialist, break both his wrists in November during a presentation for ticket agents, and in a separate incident another actor broke his foot.
Calls to Actors Equity, which represents the actors and looks after their safety on Broadway, were not immediately returned.
"I'm very disappointed in Equity," the Courier Mail quoted a source close to the union as saying.
"They seem to have been somewhat lax about safety from the beginning. They should have been in there before any of these injuries happened," the source added.
