"Nicole and her family are in shock by the sudden death of her father," Kidman's publicist and friend, Leslee Dart, said in a statement.
"She appreciates the outpouring of support and kindly requests privacy during this very difficult time."
Some media reports said Dr Kidman died after a fall at the The Tanglin Club.
Nicole's husband, country music star Keith Urban, cancelled a charity concert in Los Angeles when news came through that Dr Kidman had died.
He immediately flew by private plane to his grieving wife at their home in Nashville.
Urban was driving to the Sherwood Country Club for the $US5,000 per person event in Los Angeles on Thursday night when he was told Dr Kidman had died, according to TMZ.com.
The Australian celebrity couple is expected to fly from Tennessee to Sydney to be with Nicole's mother, Janelle, Antonia and other friends and family.
"It is with great sadness that we learn of Dr Tony Kidman's sudden passing," University of Technology vice-chancellor Professor Attila Brungs said in a statement.
"During his 43 years at the University of Technology, Sydney, Tony has contributed greatly - as a colleague, as a researcher, and as a health practitioner.
"Tony will be missed by all at UTS. Our thoughts are with his family at this time."
Urban's LA charity event was for the Ventura County Food Bank.
The event was able to get Kenny Loggins to fill in at the last moment, TMZ reported.
