Nicknamed "Blade Jumper", the 2012 Paralympics gold medallist and 2014 German national long jump champion was hoping to become the second athlete with a carbon fibre prosthesis to compete at the Olympics after South Africa's Oscar Pistorius in 2012.
However, IAAF president Sebastian Coe, speaking at a news conference where Russia's ban from the sport was extended, said: "He has to prove that the prosthetic he uses does not give him a competitive advantage and at this stage he has not been able to do that."
Rehm had commissioned a scientific study, hoping to prove he did not get an advantage, with a report last month indicating no clear edge over able-bodied athletes.
A new IAAF ruling requires amputee competitors to prove themselves they do not have an advantage over able-bodied athletes.
The study was conducted by several universities in Germany, the United States and Japan and showed that amputees such as Rehm, who lost his lower right leg in a boating accident as a teenager, had a less efficient start but a more efficient jump.
The 27-year-old jumped a para-athletics world record of 8.40 metres to win the 2015 IPC world title in Doha, a distance that would have beaten Britain's 2012 London Olympics gold medallist Greg Rutherford by nine centimetres.
(Additional reporting by Mitch Phillips and Karolos Grohmann; Editing by Toby Davis)
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