Funnell, who won team silver in Sydney in 2000 and Athens in 2004 as well as an individual bronze in 2004, had been listed previously as the team's travelling reserve on British-bred Billy the Biz.
"We are extremely disappointed for Izzy and her whole support team," said equestrian team leader Dan Hughes in a statement.
"Whilst Rio was going to be Izzy's first Olympics, as one of the most talented British riders in the world, I am confident that it will not be her last opportunity to represent Great Britain on the world stage.
"In Pippa Funnell we have an extremely strong replacement, and we are confident this team has every chance of achieving medal success in Rio."
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Funnell, 47, is a three times winner at Badminton and in 2003 became the first rider to win the Rolex Grand Slam of Eventing which involves consecutive wins in Kentucky, Badminton and Burghley.
The feat was matched this year by 2012 double Olympic champion Michael Jung of Germany.
(Reporting by Alan Baldwin, editing by Toby Davis)
