The final against Sevilla is being played at the Vicente Calderon, the home of Atletico Madrid, in the Spanish capital.
But the Community of Madrid authorities have told Barcelona that the Estelada independence flags cannot be flown.
"FC Barcelona expresses, in the most absolute terms, its total and complete disagreement with the announcement," said a statement released by the Spanish champions.
"FC Barcelona considers the decision to be an attack on the freedom of expression, the fundamental right of each and every individual to express their ideas and opinions freely and without censorship, a right which is recognized in the Universal Declaration of Human Rights."
Both Barcelona's mayor Ada Colau and the autonomous community's President Carles Puigdemont have said they are boycotting the match in protest of the ban.
L'alcaldessa @AdaColau tampoc no assistirà a la final, i contribueix a defensar un dret fonamental irrenunciable. Dignitat i llibertat.— Carles Puigdemont (@KRLS) May 19, 2016
The football club called for an immediate rethink on the ban which is likely to be enforced by body searches of Barcelona fans at the stadium.
"FC Barcelona calls for the use of common sense and responsibility and demands the government representative's cooperation in creating the good atmosphere a match such as the Copa del Rey final deserves," said the statement.
"FC Barcelona also implores the representative (of the Spanish government) to respect the honour of the institutions involved in this final and to avoid causing any uncomfortable situations."
The Estelada flag is a common sight at Barcelona games and has been a source of contention in the past.
Last year, European football's governing body Uefa fined Barca €40,000 over the flags used at a match, prompting separatist groups to then distribute thousands of the yellow and red flags at a Champions League match in protest.
Barcelona's president also threatened to take Uefa to the European Court of Human Rights over the fines.
One of Spain's 17 semi-autonomous regions with its own language and customs, Catalonia enjoys a large degree of freedom in education, health and policing.
But fed up after years of demands for greater autonomy on the taxation front - complaining it pays more to Madrid than it gets back - the region has veered towards separatism.
After winning a parliamentary majority in a regional election in Catalonia in September, pro-independence parties vowed to implement an 18-month roadmap for independence from Spain by 2017.
But while support for independence has soared in recent years in Catalonia - a region of 7.5 million people with its own language - it does not have the backing of a strong majority.
Though pro-independence parties won a majority in the 135-seat regional Catalan parliament, their share of the vote was 48 percent, giving their opponents a powerful argument against secession.