Antony Kidman, 75, died after suffering from an apparent heart attack at an exclusive social club in Singapore, local media and emergency services said.
Nicole Kidman's publicist Leslee Dart said the Hollywood actress and her family were "in shock by the sudden death of her father".
"She appreciates the outpouring of support and kindly requests privacy during this very difficult time," Dart told the Australian Associated Press in a statement.
Nashville singer Urban cancelled a concert in the United States and said he was returning to Australia with Kidman.
"We are in a deep state of grief at the passing of Nic's father and are heading to Australia to be with family," Urban said in a statement on Facebook.
"We want to thank everyone from the bottom of our hearts for their love, prayers and support through this devastating loss."
Antony Kidman was believed to have collapsed at a restaurant at the upmarket Tanglin Club, where he was staying while visiting his daughter Antonia and her family, Singapore's Straits Times said.
He was at the restaurant after exercising in the morning.
The Singapore Civil Defence Force said paramedics received a call at about 8.10am on Friday requesting medical assistance at the club and that members of public performed CPR (cardiopulmonary resuscitation).
A Singapore source told AFP on Friday that Kidman was pronounced dead at the hospital shortly after arriving.
Antony Kidman was a clinical psychologist and director of the health psychology unit at Sydney's Royal North Shore Hospital.
The family were last seen together in Sydney in January for the 50th wedding anniversary of the senior Kidman and his wife Janelle, Australian media reported Friday.
Nicole Kidman, 47, most recently starred in "Grace of Monaco", a biopic of Grace Kelly, the American film actress and Princess of Monaco.
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