Patrick Kennedy, a former congressman from Rhode Island, said his sister died Friday at a Washington-area health club.
"She's with dad," Patrick Kennedy said. Their father died in 2009 at age 77 after battling a brain tumor.
Kara Kennedy battled lung cancer since 2003, when doctors removed a malignant tumor. Patrick Kennedy said that his sister loved to exercise, but that he thinks her cancer treatment "took quite a toll on her and weakened her physically."
"Her heart gave out," he said.
Kara Kennedy was the oldest of three children. She and her brother Edward Kennedy Jr. helped run their father's U.S. Senate campaign in 1988. The National Organization on Fetal Alcohol Syndrome lists her as a national advisory board member on its website.
Edward Kennedy Jr. himself was a survivor after losing 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.
In 1990, Kara Kennedy married Michael Allen. The couple had a son and daughter, both now in their teens.
The Associated Press contributed to this report.