Real Madrid said after the game that they had requested the club's disciplinary committee to "initiate an immediate expulsion procedure for the member" who was caught on camera performing the Nazi salute.
"This member was identified by the club's security staff moments after appearing on the broadcast and was immediately expelled from the Santiago Bernabeu stadium," Real Madrid said in a statement condemning the gesture.
UEFA fined Real Madrid and also ordered the partial closure of the stadium - 500 adjacent seats of the lower south stand - for one game. However, that punishment is suspended for one year.
Real Madrid beat Benfica 2-1 and advanced to the last 16 with a 3-1 aggregate victory. They play Manchester City in the next round.