Vets ruled that her horse, Allofasudden, was not fit to compete in the three-day eventing competition that earned Jones a silver medal in Beijing 2008, because of an injury to its left fore foot.
This is the second time the Australian eventing team has replaced a competitor this month. Original rider Shane Rose pulled out on July 22 after his horse, Taurus, was also found to have a leg injury.
Jones, 35, will be replaced by Sam Griffiths, who rode in the 2010 World Equestrian Games but has never competed at Olympic level, despite being shortlisted for the Beijing and Athens Olympic Games.
Jones said she was disappointed to learn she would not be competing, adding that while she felt fine now, she would probably "fall apart" over the next few days.
"Normally he can't stop moving, and constantly weaves his head around. But all of yesterday, he stood still," Jones said, explaining how Allofasudden's injury was discovered.
"I looked him in the eyes and said: 'He's depressed.'"
She described the "pretty big rollercoaster" that she experienced this week, with the news that she would be competing coming less than a week before finding out that she would not be part of the team, after all.
In the 2010 Kentucky World Equestrian Games, Jones suffered a similar setback after her horse was diagnosed with travel sickness before the event started.
Her current situation was "on a par" with that experience, although then the disappointment was deeper because "at that stage, that's all I had".
This time Jones, who lives in Hahndorf, Australia, said that her loss was tempered with help from her fiance, whom she will marry in six months.
She said: "He's been fantastic - a pillar for me. He's actually taken it harder than me, and cried more than I have about it."
Australian equestrian section manager Brett Mace spoke of the "cruel blow" that his team had suffered, adding that Jones was a "great person, and a great supporter — we've really loved having her on our team."
The Australian team has petitioned Olympic officials to substitute reserve rider Sam Griffiths and horse Happy Times to bring their team back to full strength of five riders.
In the eventing competition, the top three scores out of five riders count for medals, with two drop scores. With only four riders, that would put Australia at a disadvantage to better their team silver won at the 2008 Beijing Games.
Australia has veteran riders Andrew Hoy, Christopher Burton, and husband/wife team Clayton and Lucinda Fredericks on their roster.
The eventing competition includes a combined score from three phases: dressage, cross-country endurance, and show jumping.