He was pulled up by jockey Dwayne Dunn on the home straight and finished nearly 41 lengths behind race winner Vow And Declare.
Vets later confirmed Rostropovich sustained a fractured pelvis but is in a stable condition.
"He couldn't weight bear," trainer David Hayes said after the race.
"But I think with a bit of painkillers, he's relieved. It's a sad story, anyway."
Rostropovich finished fifth in last year's Melbourne Cup, which was overshadowed by the death of The Cliffsofmoher.
The Cliffsofmoher was euthanised on the track after breaking down with a fractured shoulder.
Speaking about the horse, spokesperson for PETA Emily Rice told New Idea: "Rostropovich is the latest in a long line of horses who have been seriously injured or killed during the disgrace that stops the nation – the Melbourne Cup.
"While media coverage focuses on silly hats, the reality of the abusive racing industry is that horses are made to run to the detriment of their health. These 500-kilogram animals – supported on ankles as small as those of humans – are pushed past their limits, forced to race at breakneck speeds while being whipped. It's no surprise that in just one year, 122 horses died on Australian racecourses. That's an average of more than two per week, but most media reporting glosses over the bleeding lungs, broken bones, and death.
"In June, PETA revealed that some 3,000 Australian horses and their offspring had been cast off by the racing industry and killed for meat in South Korea. How many more horses have to suffer or die before we call time on this disgraceful demonstration of national senselessness?"