The 34-year-old was "strongly reprimanded" by the IOC after losing to Or Sasson in Friday's first-round bout.
The IOC said the Egyptian Olympic Committee also condemned El Shehaby and had sent him home.
However, Egypt's judo federation said he arrived home as scheduled.
Spokesman Sameh Moubasher, quoted by the AFP news agency, said: "He returned with his colleagues. The whole team judo team returned yesterday."
El Shehaby was roundly booed by the crowd and was called back to the stage for his failure to bow to his opponent as it contravenes judo rules.
Sasson later revealed his coaches had warned him El Shehaby might refuse to shake his hand as the Egyptian had come under pressure from some conservative voices in his homeland to withdraw from the bout.
The IOC said the Egyptian judoka's conduct was "against the spirit of friendship embodied in the Olympic values".
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Egyptian judoka Islam El Shehaby has been sent home from Rio after he refused to shake the hand of an Israeli opponent, the International Olympic Committee has said.