Real Madrid have begun an investigation after a supporter inside the Bernabéu was filmed appearing to perform a Nazi salute in the moments before Wednesday's game against Benfica.
The club said the fan was ejected from the ground after being identified by stadium security.
A statement said the club have asked their disciplinary committee "to initiate an immediate expulsion procedure" for the offender.
It continued: "Real Madrid condemns this type of gesture and expression that incites violence and hatred in sports and society."
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The incident came a week after Brazilian forward VinÃcius Júnior made an allegation he had been racially abused by Benfica's Gianluca Prestianni during the first leg of the Champions League play-off round tie in Lisbon, which UEFA is investigating.
Prestianni, who denies the allegation, was handed a provisional one-match ban and did not take part in Wednesday's game.
Real won 2-1 on the night and 3-1 on aggregate to reach the last 16 with VinÃcius scoring the second-half winner.
Meanwhile, LaLiga president Javier Tebas said his organisation kept a record of hate speech incidents, with abuse directed at Vinicius at the "centre" of those records.
"He is at the centre because he is the leader in this fight against racism," he told the Financial Times Business of Football Summit.
"There is no excuse for not defending Vinicius against these insults."
