The 52-year-old mother of four, who had battled drug and alcohol problems in the past, had been married to Kennedy for 16 years before he filed for divorce in 2010.
No cause of death has yet been confirmed, although American media has reported that Mrs Kennedy hanged herself. An autopsy was scheduled to take place later today.
The family later released a statement paying tribute to Mrs Kennedy, saying that they 'deeply regretted' her death.
'Her radiant and creative spirit will be sorely missed by those who loved her,' the statement added. 'Our heart goes out to her children who she loved without reservation.'
A further statement issued by Robert Kennedy Jr's chief of staff said, 'Mary inspired our family with her kindness, her love, her generous soul and her gentle spirit.'
Mrs Kennedy, who was an architect, married Robert Kennedy Jr - the third eldest of Senator Robert Kennedy's children and the nephew of former president John F Kennedy - in 1994, having known the family through his sister Kerry Kennedy whom she met at school.
The couple went on to have four children - Conor, Kyra, William and Aiden.
However Mrs Kennedy's drug and alcohol problems came to a head in 2010 - around the time that her husband filed for divorce - when she was arrested twice for suspected drunk driving.
The marriage had been the second for Robert Kennedy, who is an environmental lawyer, activist and radio show host. The 58-year-old is reportedly dating actress Cheryl Hines, best known for the TV comedy Curb Your Enthusiasm.
Mrs Kennedy's premature death is the latest tragedy to strike the Kennedy family, in what is known as 'the curse of Camelot'.
Following the assassination of John F Kennedy in 1963 a number of family members have suffered premature death or serious injury.
They include Robert Kennedy Sr, who was assassinated in 1968, his son David who died of a drug overdose in 1984 and another of his sons, Michael Kennedy, who suffered a fatal skiing accident in 1997.
John F Kennedy's son John F. Kennedy Jr was also among those who succumbed to an early death, dying in a plane crash in 1999 along with his wife Carolyn Bessette-Kennedy and sister-in-law Lauren Bessette.
More recently Kara Kennedy, daughter of Senator Ted Kennedy, died of a heart attack aged 51 following a gym workout.
