Neymar's first yellow card was for obstructing the taking of a free-kick by tying his laces, with his second booking as a outcome of a late challenge on Malaga's Roberto Rosales.
In a 2012 case similar to Neymar's, Valencia's Sofiane Feghouli was suspended three games after sarcastically applauding after his second yellow.
The red card was Neymar's first since joining Barcelona from Santos in 2013 and Luis Enrique was not convinced the attacker deserved his dismissal.
Real are now three points clear and have a game in hand despite Antoine Griezmann's strike five minutes from time snatching a 1-1 draw for Atletico Madrid at the Santiago Bernabeu.
Neymar was given two yellow cards in Barca's 2-0 loss Saturday to Malaga at La Rosaleda Stadium.
These match logs are what Spanish soccer's governing body uses to determine if players should be fined and/or given additional suspensions and, well, mocking the referee generally doesn't play well.More news: Moyes 'deserves' criticism from Sunderland supporters
Luis Enrique's side are now sat three points behind Madrid in La Liga table, with Zinedine Zidane's side drawing 1-1 against cross-city rivals Atletico earlier in the day.
The Spanish club will appeal the Royal Spanish Football Federation decision.
Real Madrid and Barcelona have both benefitted from appeal processes.
The Brazilian striker picked up two yellow cards during the defeat which would usually result in a one-match ban.
Suarez and Neymar have both failed to score against Kameni since their arrivals in Spain, with Malaga being the only La Liga side the Uruguayan is yet to score against since joining Barcelona.
As well as the Clasico, Neymar misses the home matches against Real Sociedad on April 15 and Osasuna on April 26. The extended suspension means he will miss what will potentially be the most important league game of the season, away at Real Madrid on April 23.
"It's curious that a team like us that doesn't usually kick people gets so many yellow cards in such an incomprehensible manner", Enrique said.