El Shehaby was beaten by Or Sasson in their heavyweight first round encounter but at the end of the bout, he refused to either bow to the Israeli or shake his hand.
In judo it is customary to both bow to opponents — a sign of respect in Japan — and shake hands after a bout is over.
El Shehaby had been well beaten but stood impassively as Sasson tried to shake his hand. As he left the mat area, El Shehaby was called back to the centre by the referee to bow. But he was then loudly jeered out of the arena by angry supporters.
International Judo Federation spokesman Nicolas Messner said fighters were not obliged to shake hands after a bout.
“In the past, it is not sure that a fight between those two athletes would have taken place. This is already a big improvement that Arabic countries accept to be opposed to Israel,” he said.
“There is no obligation for shaking hands at the end of the fight, but it is compulsory to bow, that’s why the Egyptian was called back to bow and he did.
“Nevertheless, his attitude will be reviewed after the Games to see if any further action should be taken.”
The 32-year-old El Shehaby, a world championship medallist in 2010, had faced pressure on social media and from hardline Islamist groups in his homeland to withdraw from the fight.
He refused to speak to journalists after his fight. Unlike some other Muslim and Arab nations, Egypt has no history of withdrawing from judo bouts against Israelis.
Sasson has faced another Egyptian, Ahmed Wahid, twice in the last year, each fighter winning once.
The Egyptian Olympic Committee had insisted before the fight that El Shehaby would compete.
On Sunday, Saudi Arabian Joud Fahmy withdrew from her 52kg first round bout against Christianne Legentil of Mauritius ahead of a possible second round clash with Gili Cohen of Israel. The Saudi Olympic Committee claimed she was injured.