The former couple met at the Robert F. Kennedy Tennis Tournament in August 1977.
As Arnold Schwarzenegger recalled in new Netflix docuseries "Arnold," the pair were first introduced at the Kennedy family tennis tournament, a charitable event that took place annually in the 1970s.
The actor had been invited to take part personally by Eunice Kennedy Shriver, Shriver's mother, and even though he had never held a tennis racket in his life, he agreed, thinking it would be good for exposure as at that point he had not yet starred in any of his career-defining movies.
"Before the actual tennis tournament, there was a big party. All of the Kennedys were there," he said. "Eunice came up to me and said, 'Oh, hi, it's so good to have you here. By the way, this is my daughter, Maria Shriver.'"
Schwarzenegger said that later on in the evening, Eunice told him that Maria was fond of him to which he cheekily replied: "Well, your daughter has a really nice ass."
"It was a stupid thing to say. I don't know why I said it," Schwarzenegger added with a laugh.
During his match, Schwarzenegger said that he could see that Shriver was intently watching him. After it was over, she and her cousin Caroline Kennedy invited the actor to spend the evening in Hyannis Port and sparks began to fly between the two of them.
At the time, Schwarzenegger was 30 years old, while Shriver was 21.