The former governor tweeted: "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."
The 13-year-old son of Schwarzenegger and Maria Shriver suffered a collapsed lung and broken bones in the July 17 accident in Malibu.
A source close to the family told ET last week that Arnold and Maria -- who are separated and in the midst of a divorce -- had been "very amicable" at the hospital while visiting their son and had been talking regularly even before the incident.