David Holmes, 25, was hurt at Leavesden Studios, near Watford, Hertfordshire, where Harry Potter and the Deathly Hallows is in pre-production.
Mr Holmes, from Romford, Essex, was taken to Watford General Hospital on Wednesday with a back injury. He has since been moved to another hospital.
His family said they were helping each other "through this difficult time."
A statement released by the family said: "We would like to thank everyone for their thoughts and prayers.
"We are trusting in the expertise of the medical staff who are caring for David."An investigation was opened by the Health and Safety Executive after the accident.