Antony died in a fatal fall during a visit to Nicole's sister Antonia Kidman in Singapore, reported Australian Associated Press (AAP).
Antony, who was close to both his daughters, was a clinical psychologist at Royal North Shore Hospital and a director of health psychology at the University of Technology Sydney.
Psychologist Dr Antony was the Director of the UTS Health Psychology Unit at Sydney's Royal North Shore Hospital.
He also ran community service seminars on aspects of mental health, was a regular speaker on radio and television and wrote for academic journals and the general public.
In June this year, Nicole walked the red carpet with her father and husband Keith Urban at the Swisse Celebrate Life Ball in Melbourne.
No official statement from his family has been released yet.