The Brazil international saw his one-match ban for a sending off in his side's 2-0 defeat to Malaga extended by a further two games earlier this month after he sarcastically applauded the fourth official while leaving the Rosaleda pitch.
On Friday, Barcelona lodged an appeal against the extension to Spain's Court of Arbitration for Sport (TAD), having seen an initial appeal rejected by the Spanish football federation.
However, TAD were unable to hold an emergency meeting on Saturday to hear the appeal as two of the committee's members could not attend.
TAD subsequently advised Barcelona that Neymar's three-match ban remained in place and that they risked sanctions if they picked an ineligible team by playing the Brazilian.
On Sunday morning, Barcelona released a statement confirming that Neymar would play no part at the Santiago Bernabeu on Sunday, but also condemned TAD's failure to hear their appeal.
The club's statement read: "Against the uncertainty due to the lack of reply from TAD with 12 hours to go until the game, and to focus all attention on sporting matters, the club have opted not to call up Neymar."
"However, Barcelona expresses its amazement at TAD's refusal to exercise its jurisdictional functions, something which directly damages both the clubs and the competition itself."
Real Madrid, top of La Liga and seeking their first title since 2012, are expected to welcome Gareth Bale back into their side.
The Wales international has completed his recovery from a muscle injury, sustained in his side's Champions League quarter-final first leg victory over Bayern Munich.
Madrid enter Sunday's game with a three-point lead over Barcelona and also hold a game in hand over their historic rivals.
Additional reporting by AP