Rehm, 27, won Paralympic gold in 2012 and is looking to become the second athlete after Oscar Pistorius to compete at the Olympics.
IAAF rules say amputee competitors must prove they do not have an advantage.
IAAF president Lord Coe said Rehm had not proven the prosthetic he uses "does not give him a competitive advantage".
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.
The study showed that amputees such as Rehm had a less efficient start but a more efficient jump.
Last year, Rehm jumped a Para-athletics world record of 8.40 metres to win the IPC world title in Doha.
That distance would have beaten Briton Greg Rutherford's winning leap at the 2012 London Olympics by nine centimetres.
Paralympic long jumper Markus Rehm is unlikely to compete at the Rio Olympics after failing to prove his prosthetic leg does not give an unfair advantage.