The match was scheduled for 26 October but there have been days of protest in Barcelona after nine Catalan separatist leaders were jailed on Monday.
Earlier this week, La Liga asked the Spanish Football Federation (RFEF) to switch the game to Madrid.
The clubs must agree a new date by Monday.
Manager Ernesto Valverde had said the Barcelona were against switching the game to Madrid as they play away to Slavia Prague in the Champions League on 23 October, three days before El Clasico had been scheduled.
La Liga made the postponement request because of "exceptional circumstances beyond our control" as more protests are expected in Barcelona on the day of the match.
Protests have continued into a fourth day in Spain's Catalonia region with protesters clashing with riot police. At least 96 people have been hurt across the region.
Catalonia is a semi-autonomous region in north-east Spain and in a referendum on 1 October 2017, declared illegal by Spain's Constitutional Court, about 90% of Catalan votes cast backed independence. Turnout was 43%.
The nine separatist leaders were convicted of sedition over their role in the referendum and handed jail sentences of between nine and 13 years by Spain's Supreme Court.