The animal belonged to Dave Galloway and was injured at the end of the first heat.
Stampede officials say there was no contact made with another horse or wagon.
"It's really upsetting to lose Ezzy," said Galloway in a release. "I try to keep my barn calm, but Ezzy was exceptionally calm. He was my fastest outriding horse and racing, for him, was effortless."
The 16-year-old thoroughbred was owned by Galloway for four years.
"The horse's injury was virtually the same as that of another outrider horse on July 11," said Stampede officials in a release. "Suspensory ligament rupture is most commonly seen in race horses and occasionally seen in other types of sport horses."
2 horse deaths due to driver error
Two other horses were euthanized following separate chuckwagon racing incidents earlier in the week.
A horse belonging to chuckwagon driver Layne Bremner suffered a broken leg during the sixth heat of the Rangeland Derby on July 4, while a crash last Monday left one of driver B.J. Carey's horses with a serious injury to a joint above its hoof.
Driver error is being blamed for the two deaths.
The Stampede brought in new rules in 2011 aimed at making chuckwagon racing safer for the horses and competitors, reducing the number of outriders running alongside each chuckwagon from four to two.
All horses are microchipped to track their health and racing records, and are not allowed to race more than three days in a row.
Each horse is inspected by veterinarians when the animals arrive at the Stampede, and before and after every race.