The four-times champion walked out of hospital with the aid of a zimmer frame in Houston, Texas, where the crash happened on Sunday.
Franchitti, 40, from Bathgate, West Lothian, was flown to Indianapolis, where he will undergo more surgery to his fractured right ankle.
He thanked hospital staff, adding: "I'm overwhelmed by the outpouring of support and I'm thankful to have such a great family and such wonderful friends and fans."
"Thanks to everyone at the hospital and the track who took such good care of me during my stay in Houston."
Franchitti admitted he is now going to put his feet up and watch the racing on TV.
He added: I look forward to watching Scott, Alex and the Target team next weekend on television, and will be pulling for them as they go for another championship."