The gelding won 23 of his 41 races, including five King George VI Chases.
The 15-year-old moved to dressage after retiring from racing in 2012.
His rider Laura Collett said: "Devastated to announce Kauto Star sustained injury in the field, with his best interest at heart a decision was made to put him to sleep."
Owner Clive Smith told BBC Radio 5 live: "It is really devastating - he was looking fit and well at Laura Collett's yard. The main injury was to the neck, as it gets worse it attacks the spinal cord. He also fractured his pelvic bone. A really sad time indeed.
"He had a great talent for never giving up. He wanted to win. With jockey Ruby Walsh riding him, he put this massive effort in at the end of races. He had a heart of a lion."
He added: "The vets made him comfortable but the kindest thing was to euthanise him. It was a horrible moment. He was such a wonderful horse, but he did not suffer."
Paul Nicholls, who trained Kauto to his famous victories, told BBC Somerset: "Kauto was such a big part of that team. We'll never have one as good as him. Sixteen Grade One wins on all those plaques [referring to those honouring the horse at his yard].
"He touched a lot of hearts. People like to follow a horse and they could do that with Kauto a number of years. You can see the reaction on social media - it's absolutely incredible."
And 20-time champion jump jockey AP McCoy told BBC Radio 5 live Kauto Star was the "complete horse".
Edward Gillespie, who was in charge of Cheltenham Racecourse during Kauto's successes in 2007 and 2009, told BBC Radio Bristol: "I was at Paul Nicholls' yard yesterday and saw the plaques for winning horses - Kauto has an entire wall.
"Some of us are old enough to remember three-time Gold Cup winner Arkle. Kauto is the only horse you can talk about in the same breath as Arkle. Racing will be mourning today."
Kauto Star became the first horse to regain the Cheltenham Gold Cup after losing it to Denman in 2008, and also made history by winning a fifth King George VI Chase,  on Boxing Day in 2011.
Walsh, who guided Kauto Star to 17 of his 23 career wins, said he had felt honoured to ride him.
"He's the horse of my lifetime. I'm very lucky to be the one who got to ride him," he said after Kauto's retirement in 2012.
"He was an amazing horse to ride and an amazing horse to be part of and I loved every minute of riding him."
Two-time Cheltenham Gold Cup winner Kauto Star has been put down after suffering neck and pelvis injuries in a fall.