The three-time Indianapolis 500 champion will travel to Indianapolis, where his Target Chip Ganassi Racing team is based, for a second surgery on his right ankle, IndyCar said on its website.
Franchitti's car went airborne and destroyed a portion of the catch fence before spinning several times while debris injured several spectators after he made contact with Japanese driver Takuma Sato on the final lap.
"I'm overwhelmed by the outpouring of support and I'm thankful to have such a great family and such wonderful friends and fans," said Franchitti.
"Thanks to everyone at the hospital and the track who took such good care of me during my stay in Houston."
The 40-year-old Briton will be replaced by Alex Tagliani in IndyCar's Oct. 19 season finale in Fontana, California.