Kobak, who works under the stage name Joshua Kobak, clams to have suffered two knee injuries, herniated discs, whiplash and a concussion from two separate incidents.
The actor was allegedly hurt performing the same aerial stunt that hospitalised cast member Christopher Tierney in December last year. Kobak says that the computer rigging system was not reprogrammed for his weight, causing the accident in which he sustained the knee injuries.
He also claims that another computer rigging error propelled him into a wall during another stunt sequence, causing the other injuries listed in the report, Variety understands.
Kobak has taken action against the musical's executives through the New York State Supreme Court, and is demanding that they turn over documents containing details of the accidents and the controls to the on-stage equipment.
Spider-Man: Turn Off the Dark overcame a troubled development cycle to break box office records in January, achieving the highest-ever single-week gross of any Broadway musical in history.
The show's producers are yet to respond to Kobak's allegations.