The 47-year-old was involved in the "terrifying" crash in the Bergrennen Hemberg race on Saturday but avoided serious injuries.
Photos have emerged on social media showing a wrecked car in flames that the TV star was reportedly driving.
It is believed he was driving a £2 million supercar for the Amazon show The Grand Tour before it burst into flames.
Co-star Jeremy Clarkson tweeted that despite the "frightening" crash, Mr Hammond seems to be "mostly okay".
Images on the race's official Instagram showed vehicles drifting rally-style around a tarmac track.
A source told the Sun: “Richard is conscious but very shaken.
“He is currently being treated in hospital for a fractured knee and having the once over. It’s quite incredible he’s come away from this with nothing more serious quite frankly.
It was the biggest crash I've ever seen and the most frightening but incredibly, and thankfully, Richard seems to be mostly OK.— Jeremy Clarkson (@JeremyClarkson) June 10, 2017
"The crash was really bad. The car completely flipped and then burst into flames.
"There was real concern for Richard but the emergency services were quickly on hand and he’s a very lucky boy.
"It brought back horrendous memories of the 2006 crash for those who witnessed it."
It is the second time that Mr Hammond has been involved in a serious crash, having been left in a coma following a crash at 288mph in 2006.
He was filming an episode of Top Gear at the time.
Jeremy Clarkson tweeted: "It was the biggest crash I've ever seen and the most frightening but incredibly, and thankfully, Richard seems to be mostly OK."
Mr Hammond was in Switzerland filming new episodes for the series The Grand Tour, which he co-stars in alongside Jeremy Clarkson and James May.
The show's statement said: "Richard Hammond was involved in a serious crash after completing the Hemburg Hill Climb in Switzerland in a Rimac Concept One, an electric super car built in Croatia, during filming for The Grand Tour Season 2 on Amazon Prime, but very fortunately suffered no serious injury."
"Nobody else was in the car or involved in the accident, and we'd like to thank the paramedics on site for their swift response. The cause of the crash is unknown and is being investigated," the statement added.
In March this year, Hammond assured fans he was fine after falling off a motorbike "many times" while filming for The Grand Tour.
He was in a remote part of Mozambique in east Africa shooting the programme when the accident occurred, according to The Sun.