Schwarzenegger was photographed arriving at the hospital yesterday to join Shriver at 13-year-old Christopher's bedside, the Daily Mail reports.
The couple released a joint statement which read: "A few days ago, our son Christopher suffered an accident at the beach.
"While it has been a very scary week, Christopher is surrounded by his family and friends. He is a brave boy and is expected to make a full recovery."
Christopher is thought to have suffered multiple broken bones and a collapsed lung in the accident in Malibu last weekend.
Schwarzenegger and Shriver also appealed for privacy in their statement, adding: "On behalf of our entire family, we want to sincerely thank the paramedics and lifeguards who responded so swiftly as well as the doctors, nurses, emergency room and hospital staff who have cared for our son. They have been extraordinary to him and to us.
"We thank everyone for their thoughts and prayers."
Shriver and Schwarzenegger announced their separation in May after 25 years of marriage.