"She's with Dad," said her brother, a former congressman from Rhode Island. Their father, who had a malignant brain tumor, died in 2009 at age 77.
Her mother, Joan Kennedy, told the Boston Globe that Kara's death was "such a shock because she was in such good health."
"She swam I don't know how many miles. She was in wonderful health," said her mother, who was the senator's first wife.
In 2005, her mother had surgery for breast cancer. Her other brother, Edward Kennedy Jr., lost a leg to bone cancer as a child. And Patrick Kennedy had surgery in 1988 to remove a non-cancerous tumor that was pressing against his spine.
Kara Kennedy was a filmmaker and television producer who produced several videos for Very Special Arts, an organization founded by her aunt, Jean Kennedy Smith. Kennedy also served as a director emeritus and national trustee of the John F. Kennedy Library Foundation and was on the board of the Edward M. Kennedy Institute for the United States Senate.
Kara Ann Kennedy was born Feb. 27, 1960, in Bronxville, N.Y., as her father campaigned for his brother, John F. Kennedy, during the presidential primaries.
"I had never seen a more beautiful baby, nor been happier in my life," the senator wrote in his 2009 memoir, "True Compass."
Kara's name meant "little dear one," the senator wrote.
A graduate of Tufts University, she kept a low public profile as an adult.
In 1990, she married Michael Allen, a professional sailor. They later divorced. Their two children, Grace and Max, are in their teens.
When her father was awarded the Presidential Medal of Freedom in 2009, shortly before he died, Kara accepted it on his behalf.
In honor of the groundbreaking for the Edward M. Kennedy Institute, Kara wrote an article in April for the Boston Globe about growing up in a family that emphasized public service.
She recalled annual family "historical road trips" that her father led, teaching his children "that a single person can always make a difference."
Kennedy's survivors include her two children, her mother and two brothers.