Real Madrid say they will take legal action against any fans found to have attacked players' cars, including that of Wales international Gareth Bale.
Spanish TV appeared to capture images of fans striking the white Bentley of Bale and team-mate Jese Rodriguez's car after Sunday's 2-1 defeat by Barcelona.
"Real Madrid will take any applicable legal action against the individuals responsible," a club statement said.
Real said one club member had been suspended pending an investigation.
The club added it had already identified the individuals responsible for what it called "aggressive and violent actions against several of our players".
The team arrived back in Madrid in the early hours of Monday following their El Clasico defeat in Barcelona.
Bale, who had a goal disallowed in the first half but struggled to make an impact after the break, was driving away from the training camp when the attack apparently happened.
The Welshman has been the subject of some criticism over his form in the Spanish media, although he scored two goals against Levante on 15 March.