Players including Wales winger Gareth Bale and forward Jese were targeted along with coach Carlo Ancelotti after they arrived back in Madrid following the 2-1 defeat at the Nou Camp.
The government's anti-violence in sport commission imposed the fines as well as a six-month ban from sports installations, the commission said on Thursday.
Real said on Monday one of the three men had been identified as a member and had been suspended and banned from their facilities pending a disciplinary hearing on whether to expel him from the club.
Second-placed Real's defeat left them four points behind leaders Barca with 10 games left.
(Reporting by Iain Rogers, editing by Toby Davis)
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