Christopher, 13, was taken to hospital after suffering broken bones and a collapsed lung in the accident in Malibu.
Schwarzenegger wrote on Twitter: "Thanks for all your support for Christopher. It means a lot to me & to him. He's doing much better & we'll have him back at full speed soon. (sic)"
The former California governor and estranged wife Maria Shriver previously released a joint statement saying that the teenager is expected to make a "full recovery".
"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 added.
"They have been extraordinary to him and to us. We thank everyone for their thoughts and prayers."
The former couple's son Patrick also provided an update on Christopher, writing on his own Twitter account: "My brother is doing a lot better."
Schwarzenegger and Shriver separated in May after 25 years of marriage.