Franchitti's Target Chip Ganassi Racing team announced the 40-year-old had been allowed home from the Memorial Hermann Texas Medical Center in Houston, where he has been undergoing treatment since Sunday's last-lap accident.
He will travel to Indianapolis for further evaluation, with a second operation on a right ankle fracture in the pipeline.
Franchitti underwent a first operation on his ankle in the hours immediately following Sunday's crash. He also suffered a concussion and fractured vertebrae that will not require surgery.
"I'm overwhelmed by the outpouring of support and I'm thankful to have such a great family and such wonderful friends and fans," Franchitti, a four-time IndyCar champion and three-time Indianapolis 500 winner, said in a statement released by his team.
"Thanks to everyone at the hospital and the track who took such good care of me during my stay in Houston."
Franchitti will be replaced in the Chip Ganassi team by veteran racer Alex Tagliani for the season finale in Fontana this weekend.