The crash site was quickly surrounded Thursday by event staff members who concealed the downed horses with tarps, witnesses posted on Twitter.
The incident involved only one chuckwagon, driven by Chad Harden.
Of his four horses, the left lead horse went down at full gallop, pulling the others down as well, the Calgary Sun said.
One of Harden's two outriders behind him rammed into the back of the wagon and was thrown through the air. He was not seriously injured, the Calgary Herald reported.
Within seconds, veterinary staff members were on the track.
The horse that collapsed was dead, but the right lead horse and the 18-year-old outrider horse were euthanized on the track, the newspapers said.
Veterinarian Greg Evans told the Sun all the horses involved had been examined and tested before the race as part of new safety protocols.
The accident provides more fodder for groups calling for an end to the largest rodeo event in the world. One of the most vocal opponents is the Vancouver Humane Society, which has said more than 50 horses have died at the stampede since 1986 "for entertainment value."
Britain banned rodeos in 1934 because of cruelty concerns.