The statement gave few details of the mishap involving Christopher Schwarzenegger, the youngest of the couple's four children, nor did it say how badly he was hurt.
But the celebrity news website TMZ.com reported the youth was severely injured when hit by a large wave while surfing or boogie-boarding last weekend in Malibu, suffering multiple broken bones and a collapsed lung.
According to TMZ, the boy initially was hospitalized in intensive care, but his condition has since been upgraded.
His parents said their son is expected to make a full recovery.
"While it has been a very scary week, Christopher is surrounded by his family and friends," the couple's statement said.
"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."
Shriver filed for divorce from Schwarzenegger on July 1, weeks after the Austrian-born former bodybuilder and film star publicly admitted to fathering a child out of wedlock with a member of the family's household staff more than a decade earlier. Schwarzenegger and Shriver had separated in May.
Shriver, a daughter of the Kennedy political dynasty, gave up her career as a network television journalist when she became California's first lady at the start of Schwarzenegger's two terms as governor. She has requested spousal support and joint custody of all their children.
Schwarzenegger's attorney filed court papers on Wednesday seeking suspension of court-ordered spousal support to Shriver and requesting that she pay her own legal fees, according to legal documents obtained by Reuters.
Two of Christopher's siblings, Katherine, 21, and Patrick, 17, posted messages of support for their younger brother on Twitter on Friday.
"This kid is strongest kid I ever seen (sic). Keep praying," wrote Patrick, while Katherine wrote: "He's a tough little guy and getting better!"
(Reporting by Mary Slosson; Editing by Steve Gorman, Jerry Norton and Cynthia Johnston)
