They released a joint statement Monday night:
"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.
"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."
Arnold, a movie star and former governor of California, and Maria, an author, former TV reporter and ex-first lady of California, have been married for 25 years.