Shriver, 55, moved out of their Brentwood, Calif. mansion and has been living apart from the Terminator actor for a "few weeks," according to the paper. The couple, who wed in 1986, have four children together: Katherine, 21, Christina, 19, Patrick, 17 and Christopher, 13.
"This has been a time of great personal and professional transition for each of us," the couple said in a statement obtained by the Times. "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," the couple added. "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 news comes during a big transition period for the couple. Schwarzenegger, 63, stepped down as the Governor of California in January after serving two terms as the head of state. Shriver, a former TV journalist for NBC and the niece of President John F. Kennedy, lost her father in January.
Schwarzenegger recently announced a collaboration with comic book writer Stan Lee and signed on for several new films, including a new Terminator sequel.