The death came four days after his father's girlfriend, 32-year-old Rebecca Nalepa, had been found dead hanging from a balcony in the house, authorities said.
"With great sadness, Dina and I convey the tragic passing of our beloved son, Max (affectionately known as Maxie)," the statement issued through Medicis Pharmaceuticals said. "Despite heroic efforts on the part of paramedics and hospital staff, he was unable to recover from the injuries suffered early last week. His loving, kind and vibrant spirit will be forever in our hearts and those whom he touched every day."
On Monday, Max fell down the stairs at the historic Spreckels mansion in Coronado in what police called a tragic accident. He was not breathing and did not have a pulse when paramedics found him and took him to Rady Children's hospital.
On Wednesday, officials said Shacknai's 32-year-old girlfriend, Rebecca Nalepa, was found dead hanging nude from a balcony at the mansion, her hands and feet bound. Shacknai's brother, Adam, who was staying in the mansion guesthouse, called to report Nalepa appeared to be dead, police said. Jonah Shacknai was not at home.
Sheriff's Capt. Tim Curran has called the death "very bizarre."
Sheriff's investigators said last week they have not established any connection between the two deaths, and have not determined if Nalepa was a crime victim and have made no arrests. They said they have not ruled out suicide.
Phone messages left late Sunday with sheriff's homicide investigators were not immediately returned.
The 27-room Spreckels mansion was built in 1908 in the wealthy seaside suburb of about 24,000 people on San Diego Bay.
Coronado had just one homicide last year, and the police department asked the sheriff's department to help with the investigation.
Jonah Shacknai, 54, founded Medicis, based in Scottsdale, Ariz., and has been chairman and CEO since 1988.