The Stampede said driver Tim Haroldson was a passenger on a wagon driven by fellow driver Jerry Bremner.
The wagon rolled Tuesday while coming around one of the barrels during training, and Haroldson was thrown.
He was taken to hospital for evaluation and treatment.
Bremner was not injured.
In a separate incident, a 12-year-old horse belonging to the team of Reg Johnstone collapsed after completing a run.
No other horses were injured.
"We are hoping for the best for Tim," Paul Rosenberg, vice-president programming at the Calgary Stampede, said in a news release.
The Stampede is reviewing the circumstances of the crash to determine what happened. Initial indications are that there was nothing out of the ordinary with the wagon, the horses or the tack.
The Stampede said the horse that died, which was named Denny, had last raced about a week ago at the Ponoka Stampede.
Late Tuesday, the Stampede said on its website that an autopsy has determined the horse died of a ruptured aneurysm.
The death of the horse prompted the Canadian Federation of Humane Societies to call on the Calgary Stampede to immediately end the annual chuckwagon races.
The federation said since 1986 at least 60 animals have died or been injured at the event, half of which have been related to the chuckwagon races.
"Ironically, chuckwagon racing is not an event that is recognized by the Canadian Professional Rodeo Association," the federation said in a release.
"The sole purpose of the chuckwagon races appears to be excitement, show and entertainment at the expense of the life of an animal."
The federation said chuckwagon races reflect a shift in tradition from protecting the welfare of horses to profiting from their stress and suffering.
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