The more infamous of the pair, with housekeeper Mildred Baena, resulted in a child who's now a teenager, it was revealed last year.
In an interview with 60 Minutes to promote the book, Schwarzenegger calls his infidelity "the stupidest thing I've done in the whole relationship."
"It was terrible," the former governor of California admits. "I inflicted tremendous pain on Maria and unbelievable pain on the kids."
Shriver filed for divorce in May 2011 after learning that Schwarzenegger had fathered a child with Baena. The couple were married for 25 years.
Schwarzenegger's full 60 Minutes interview airs Sunday at 7/6c on CBS. Watch a clip below:A video or other embedded content has been hidden. Click here to view it.