Tim Tierney said his son Christopher was able to walk with a brace and has now been discharged from hospital to a
The actor suffered a skull fracture and cracked vertebrae when he fell 30 feet during a show on 20 December.
Spider-Man: Turn Off the Dark features music by Bono and The Edge of U2.
Christopher Tierney's accident is one of several to have befallen the show, thought to be the most expensive musical staged on Broadway.
Video of the incident showed him falling from a ledge into the stage pit, despite wearing a safety harness.
Two preview performances were cancelled as new safety procedures were put in place.
New precautions for the show, which features nearly 40 aerial stunts, now requires a second person to check harnesses after they have been put on.
Meanwhile, lead actress Natalie Mendoza announced on Thursday she was pulling out of the show.
The actress, who appeared in BBC drama Hotel
featured in horror film The Descent and its sequel Mendoza
Having recently returned to the show, she withdrew following several days of negotiations.
The actress cited her head injury as the reason for her departure.
"It has been a difficult decision to make, but I regret that I am unable to continue on Spider-Man as I recover from my injury,"
The $65m (£42m) production is to hold its official opening night on 7 February. Its producers said
It is believed one of two understudies for
The musical is directed by Julie Taymor, whose previous shows include the musical adaptation of Disney film The Lion King.
Despite a deluge of negative publicity, business has been brisk at