The 13 year old has been treated in a hospital intensive care unit (ICU) after suffering multiple broken bones and a collapsed lung during the incident in Malibu, California.
The Terminator star has now taken to his Twitter.com page to give an update on the teen's progress and thank followers for their well wishes.
He writes, ""Thanks for all your support for Christopher. It means a lot to me and to him. He's doing much better, and we'll have him back at full speed soon.""
Schwarzenegger's elder son Patrick also tweeted a photo of himself wearing a T-shirt with Christopher's face on it, with the caption: ""My brother is doing a lot better. Wearing this shirt for him.""