"With great sadness, Dina (Shacknai's ex-wife and the boy's mother) and I convey the tragic passing of our beloved son, Max," Shacknai says in the statement.
"Despite heroic efforts on the part of paramedics and hospital staff, he was unable to recover from the injuries suffered early last week."
Last Monday, Max Shacknai fell down the stairs of the mansion and remained in the hospital until his death Friday.
Shacknai's son's death comes just days after the body of 32-year-old Rebecca Nalepa -- Shacknai's girlfriend -- was
found in the courtyard of the
mansion with a rope around her neck, bound, naked, and hanging from a
It remains unclear whether Nalepa was murdered or committed suicide, and San Diego police say it's one of the most "bizarre" deaths they've ever seen.
Just before 7 a.m. Wednesday, police received a call from Adam Shacknai,
Jonah Shacknai's brother, saying that a woman was possibly dead at
Adam Shacknai found Nalepa hanging from a balcony in the courtyard of the Coronado mansion and cut her down.
When police arrived, Nalepa was lying on her back. Her feet and wrists were bound.
Authorities say an autopsy has been completed but that the results are currently sealed.
Jonah Shacknai, police say, was not in the home when Nalepa's body was found.
Shacknai has been the chairman and chief executive officer of the Scottsdale-based Medicis pharmaceutical company since 1988.
Medicis sells the acne drug Solodyn and cosmetic products like Restylane and the botulinum toxin Dysport, a Botox competitor.
"The Medicis family is deeply saddened to learn of a tragic incident at a California property owned by Jonah Shacknai," the company says in a statement. "Our thoughts are with Jonah and his family and (we) ask that the family's privacy be respected during this difficult period. At this time, the company has no further comment."
Authorities continue to investigate the strange death.