Hammond was filming an episode of the Grand Tour series for Amazon Prime with colleagues James May and Jeremy Clarkson in Hemberg, in the canton of St Gallen, on the course of the Bergrennen hill climb race.
Driving a Rimac electric supercar, the presenter lost control on a bend, causing the car to skid down a slope and flip over, before bursting into flames.
Hammond managed to escape the car before the fire started, but suffered a fracture to his knee.
He was airlifted to hospital in St Gallen, from where he posted a video message entitled ‘I’m not dead’ on Sunday.
In it he thanked the emergency services and medical staff who were preparing to give him a “Swiss army knee” in an operation later that day.
He also said sorry to his wife and daughters for being a “colossal...” at which point his message was interrupted by someone holding a copy of a book entitled ‘The Idiot Brain’ to camera.
In a separate post, co-presenter Clarkson said immediately after the crash no one knew if Hammond had been able to get out before the car burst into flames.
“And I can feel it now; the coldness. My knees turning to jelly,” he said.
He later tweeted it was "the biggest crash I've ever seen".
In 2006 Hammond, now 47, was left in a coma for two weeks after a high-speed crash whilst filming for Top Gear near York, UK.
Though he suffered brain injuries he went on to make a full recovery.