Rose, a silver medallist in three-day eventing at the 2008 Beijing Games, will be replaced by travelling reserve Megan Jones and her horse, Allofasudden. Her inclusion is subject to IOC approval.
Australian equestrian section manager Brett Mace said the injury to Taurus was already known, but the team had hoped the horse would recover in time for the games.
"While the injury is not serious, there is just not enough time for recovery with just under a week to go," Mace said.
"There is no doubt this is a blow for the team," Mace said. "We feel for Shane, who has worked for many years preparing Taurus for these games. He is a hard working athlete who was a formidable part of our silver medal Beijing team."
Jones also won silver in Beijing in the team event and finished fourth in the individual event.
The last time Australian reserves were substituted into the eventing team was in 1992 and 1996, when Gill Rolton stepped in. Both teams went on to win gold.