Players including Wales winger Gareth Bale and forward Jese were targeted along with coach Carlo Ancelotti after they arrived back in Madrid following their 2-1 defeat at Barcelona in the La Liga 'Clasico'.
Footage published in Spanish media showed one man striking Jese's car window and yelling insults. When Bale and Ancelotti left they were also insulted and two men tried to punch and kick Bale's vehicle as security guards looked on.
Sergio Ramos, one of the club captains, briefly stopped to ask the men what they were doing before driving on.
Real said on their website on Monday one of the three men had been identified as a club member and had been suspended pending a disciplinary committee hearing which would decide whether or not to expel him.
"Real Madrid has also informed the National Antiviolence Commission of the incidents and identified the perpetrators, asking that the sanctions they consider appropriate be applied," they added.
Real's defeat at the Nou Camp left them four points behind leaders Barca with 10 games left.
(Reporting by Iain Rogers, editing by Justin Palmer)
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