Shriver was born on July 10, 1921, the middle child of the nine children of Joseph P Kennedy Sr and his wife, Rose.
Shriver's brother Edward Kennedy, a senator for Massachusetts, said that she had a "boundless passion to make a difference" from an early age.
"Though the Special Olympics will be her enduring monument, in our family she'll be remembered as a loyal and loving sister, a treasured wife to Sarge, and a wonderful mother and grandmother," he said in a statement.
Two of Shriver’s siblings were assassinated during the 1960s.
John F Kennedy was shot dead in 1963 as his presidential motorcade travelled through Dallas, Texas. Robert Kennedy was assassinated in California in 1968.
Shriver was deeply involved in her brothers' political campaigns but her advocacy work transcended the Democrat-Republican party line.
Republican President Ronald Reagan praised her "enormous conviction and unrelenting effort ... on behalf of America's least powerful people" in 1984 when he awarded her the Presidential Medal of Freedom, the nation's highest civilian honour.
Shriver founded the Special Olympic Games in 1968 as part of her advocacy work for the mentally handicapped.
At least 190 nations now take part in the games, more than 40 years after the first US Special Olympics was held.
Earlier in her professional life, she worked for the US state department and with female prisoners in West Virginia.
Shriver was married to Sargent Shriver, whose public service included starting the Peace Corps under John F Kennedy.
She campaigned with her husband when he was the vice-presidential candidate with George McGovern in 1972 and when he ran for the Democratic nomination for president in 1976.