Shriver, who founded the U.S. Peace Corps in the early 1960s before becoming a leading American philanthropist and beloved politician, was father to Schwarzenegger's wife Maria Shriver.
He was also a one-time U.S. vice-presidential candidate.
Shriver announced he was battling Alzheimer's disease in 2003.
A statement from President Barack Obama reads, "I was deeply saddened to learn about the passing of Sargent Shriver, one of the brightest lights of the greatest generation. Over the course of his long and distinguished career, Sarge came to embody the idea of public service.
"Of his many enduring contributions, he will perhaps best be remembered as the founding director of the Peace Corps, helping make it possible for generations of Americans to serve as ambassadors of goodwill abroad. His loss will be felt in all of the communities around the world that have been touched by Peace Corps volunteers over the past half century and all of the lives that have been made better by his efforts to address inequality and injustice here at home."
Shriver is survived by his five children with late wife Eunice, who died in 2009.