She was the daughter of Robert and his wife Ethel Kennedy's fifth child, Courtney.
Emergency crews were called to a medical emergency at the Kennedy compound in Hyannis Port, Massachusetts, on Thursday afternoon, according to the Hyannis Fire Department.
By the time medics arrived to the Marchant Avenue mansion, the young Kennedy was already in cardiac arrest, the Hyannis News reported. She was pronounced dead at Cape Cod Hospital.
"Our hearts are shattered by the loss of our beloved Saoirse," the Kennedy family said in a statement released to local media. "Her life was filled with hope, promise and love."
Her grandmother, Ethel Kennedy, said in the statement: "The world is a little less beautiful today."
The family statement made no mention of a possible cause of death. However, US media reports cited law enforcement officials as saying that the death was apparently due to drug overdose.
Saoirse had volunteered in Mexico to build schools in indigenous communities and was "moved by the causes of human rights and women's empowerment", her family said.
She was a communications major at Boston College and had suffered from depression, reports said.
"My depression took root in the beginning of my middle school years and will be with me for the rest of my life," she wrote in a student newspaper in 2016.
The Kennedy family has seen a number of tragedies including the assassination of Hill's grandfather. Saoirse's grandfather, like his brother, former President John F. Kennedy, was fatally shot by an assassin, in 1968.
Her uncle David Kennedy died of a cocaine overdose in a Palm Beach, Florida, hotel room in 1984.
Another uncle, Michael, was killed in 1997 when he accidentally skied into a tree.
JFK's son, John F. Kennedy Jr., died in 1999 when his plane crashed into the Atlantic Ocean off the coast of Martha's Vineyard. His wife and sister-in-law were also on board and died.
Fifty years ago, Senator Ted Kennedy's car plunged off a bridge on Martha's Vineyard, and his 28-year-old passenger, Mary Jo Kopechne, died.
( With inputs from IANS )