Shriver, who tied the knot with Schwarzenegger in 1986, moved out of their Brentwood, California home a few weeks ago, reports the Los Angeles Times.
However, the two will take care of their four children together and are working "on the future" of their relationship, reports contactmusic.com.
"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," they said in a joint statement.
"We are continuing to parent our four children together. They are the light and the center of both of our lives. 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."
