The statement called it "a very scary week."
The teen suffered a collapsed lung and broken bones in the accident that took place "a few days ago."
Two of his siblings tweeted about their 13-year-old brother: sister Katherine says "he's a tough little guy and getting better" and brother Patrick says "keep praying."
The statement thanked paramedics, lifeguards, doctors and hospital staff who have cared for the injured teen.
The statement was issued by the former California governor and Shriver. The couple are separated and in the midst of a divorce.