The federation previously requested that the match should be moved to Real Madrid's Santiago Bernabeu stadium but the request was diligently rejected by both clubs.
Earlier this week, Spanish Supreme Court jailed nine Catalan separatist leaders for between nine and 13 years for their role in an illegal referendum and subsequent failed independence bid.
La Liga champions, Barcelona, condemned the court judgement on Monday with a statement insisting "prison sentences are not the solution".
The Spanish League feared a match of this magnitude could be used by protestors to stage further acts of unrest.
Both Barcelona and Real Madrid have now been told that they have until Monday, at 10:00am (CET) to agree on a new date, otherwise a date will be chosen for them by La Liga.
The RFEF said in a statement: "Following an extraordinary meeting yesterday by the RFEF Competition Committee, an analysis of the Liga match between Barcelona and Real Madrid scheduled for October 26 has resulted in the following”.
"The rules prevent the alteration of the order of matches between the teams already in the calendar”.
"The Committee will allow the affected clubs to reach an agreement on a new date for El Clasico. Barcelona and Real Madrid are requested to select a date and time in the coming hours, with Monday, October 21 at 10:00am (CET) as a limit”.
"In the case that an agreement cannot be reached, the Competition Committee will be the body responsible for determining the date of the match”
