Actor Schwarzenegger, who is a former governor of the state of California, and Peabody Award-winning journalist and author Shriver released a joint statement to the press following speculation that the couple were living separately.
The statement read: "This has been a time of great personal and professional transition for each of us. After a great deal of thought, reflection, discussion and prayer, we came to this decision together. At this time, we are living apart while we work on the future of our relationship."
Schwarzenegger and Shriver also confirmed that they would continue to share parental responsibility for their four children, describing them as "the light and the centre of both of our lives".
They continued: "We consider this a private matter and neither we nor any of our friends or family will have further comment. We ask for compassion and respect from the media and the public."
The couple were introduced in the late 1970s by journalist Tom Brokaw at a charity event. They married in April 1986.
It was recently reported that Schwarzenegger had signed on for a Terminator sequel in addition to the drama Cry Macho. He was presented with the Legion of Honour, the highest prize by the French government, earlier this year.