A statement from her brother, U.S. Sen. Edward Kennedy, D-Mass., said Lawford died Sunday at her home in Southampton, N.Y., of complications of pneumonia.
She was one of four of Joseph and Rose Kennedy's surviving children of nine in total, The Washington Post reported.
In 1954, she married Peter Lawford, whom she had met through John Kennedy, but divorced in 1966, after having four children.
She was politically active, and during John Kennedy's first campaign for Congress, she, her sisters and their mother held tea parties to tell voters of the future president's childhood.
She also played a role in the Senate campaigns of her brothers Robert and Edward, the family statement said.
As well as her children, she is survived by two sisters, Eunice and Jean, the newspaper said.