The accident occurred at the beginning of the second act. Daniel Curry, a graduate of the LaGuardia School of Performing Arts - the so-called "Fame" school - and who appeared in an episode of "Smash" and toured with the "Man In The Mirror" Michael Jackson Tribute tour, is making his Broadway debut in the show.
He is one of several actors who plays the costumed Spider-Man during each performance, leaping into the audience and swinging over the orchestra. He also understudied various other roles.
"Something happened with the stage, where one of the actors, we think his leg, when the stage came up, was crushed," one theatergoer said. "So they stopped the play."
Others then rushed to help Curry, and the performance was halted.
"Someone came on the stage, stopped everything," another audience member said. "People ran up on the stage, and his foot obviously got caught in one of the elevators, the floor lifts that bring them up to the stage."
A spokesman for the show said Curry was taken to Bellevue Hospital, where he received medical attention.
Producers blamed the accident on human error and the union representing actors vowed to investigate.
"Tonight's performance will go on as scheduled. The technical elements of the show are all in good working order, and we can confirm that equipment malfunction was not a factor in the incident," said Rick Miramontez, a show spokesman.
This isn't the first time injuries have affected the show. In 2010, actor Christopher Tierney fell more than 20 feet from a platform and suffered a fractured skull, a fractured shoulder blade, four broken ribs and three broken vertebrae.
During the show's run, which is filled with elaborate technical effects and equipment, several other actors have been injured. A lead actress, Natalie Mendoza, suffered a concussion during the first preview performance and left the show. A stuntman, Richard Kobak, sued the producers, saying he suffered a concussion, whiplash and two holes in his knees.
Audience members who purchased their tickets through Ticketmaster were told they would get a refund.
Plans were being made to refund the rest.
Curry, who is in his 20s, was raised near Minneapolis and told The Star-Tribune in 2011 that he thirsted for a life performing in New York. His mother soon moved the family to Queens.
"I had these big dreams," he said. "I've always wanted to dance, to be on Broadway, and I'm just thankful for my mom for making that happen."
"Spider-Man: Turn Off the Dark" is Broadway's most expensive show and has become one of its biggest hits after a rocky start, with six delays in its opening night, a shake-up that led to the firing of Julie Taymor, the show's original director, and critical drubbing.
(The Associated Press contributed to this story)