Tim Tierney said Christmas morning that his son is spending the holiday with his mother and brother in the hospital while recovering from back surgery.
The actor's father says director Julie Taymor came to visit his son in the hospital on Christmas Eve.
Tierney is the show's main aerialist and performs stunts for the roles of Spider-Man, and the villains Meeks and Kraven.
Christine Bord of Clinton, N.Y., was sitting behind a perch on the balcony when the accident happened. The actors who fly over the audience stop on that small ramp.
"It looks like part of the New York City skyline ... like a building and Spider-Man was up on the top of that ... ramp," she said. "The actress who was playing Mary Jane came off of that at the bottom. In the scene, of course, Spider-Man was supposed to come down and we're assuming save Mary Jane at the end of the scene but instead he came flying down and he just slid right off the bottom of that ramp into the pit below and came tumbling down into the stage.
"He was being held up by a wire and you could see at the end of the wire there was maybe a weight or something that kind of came following after him," Bord said. "And then after they both came down, it was just silent and you started to hear people screaming in the pit."
The production has been under investigation by the federal Occupational Safety and Health Administration for several weeks, according to the agency.
The $65 million musical was conceived by Tony Award-winning director and co-writer Julie Taymor and U2's Bono and The Edge, who wrote the music. More than eight years in the making, delays and money woes have plagued the show's launch. Three other accidents have injured actors, including one who had both his wrists broken while practicing an aerial stunt.
The show's massive costs - a 41-member cast, 18 orchestra members, complicated sets and 27 daring aerial stunts, including a battle between two characters over the audience - mean the 1,928-seat theater will have to virtually sell out every show for several years just to break even. The weekly running bill has been put as high as $1 million. (Tickets are priced from $67.50-$135 for weekday performances and $67.50-$140 for weekend performances.)
The Associated Press contributed to this report