The Aidan O'Brien-trained horse suffered a fractured shoulder during Tuesday's race and had to be euthanised, Racing Victoria's executive general manager of integrity services, Jamie Stier, said in a statement.
"The horse received immediate veterinary care, however it was unable to be saved due to the nature of the injury sustained".
Cross Counter was the final victor of the Melbourne Cup after a nail-biting final, taking the lead in the very last seconds of the home stretch.
Jockey Ryan Moore checks on The Cliffsofmoher after it broke down in the first lap of the Melbourne Cup.
The Cliffsofmoher's jockey Ryan Moore looks dejected as he walks off the track, while Cross Counter's win in the Melbourne Cup plays on the big screen behind him. "He's really sweating up badly", horseracing commentator and Sports Sunday panellist Richard Freedman said before the race.
A deluge of rain made for a treacherous start to Melbourne Cup day, forcing delays to races and trains to Flemington Racecourse, and leading to calls for the $7.3 million feature race to be cancelled.
World Animal Protection also condemned the incident, labelling the Melbourne Cup a "disgrace".
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It also sparked speculation that O'Rourke could use an upset of Cruz, or even a close loss, to run for president in 2020. Secretary of State data through Thursday includes counties that are home to almost 80 percent of Texas' population.
The son of Galileo was owned by Nick Williams, son of horseracing icon Lloyd Williams.
French-trained horse Verema had to be put down after an injury suffered in the 2013 Cup.
In the same 2014 race, import Araldo had to be euthanised because of an injury suffered when he was returning to scale.
The horse clipped the heels of another runner and injured a foreleg when falling as the field turned for home.
The following year fan favourite Red Cadeaux shattered a leg and was put down on the track.
Ladbrokes' website and app also went down in the run-up to last year's Melbourne Cup Day, setting off a storm of social media complaints from punters.