The state Higher Sports Council proposed the sanctions for "behaviour whose aim was to transform the sporting event into a stage for political demands through intolerant acts".
These included "whistling the national anthem and His Majesty the King", patron of the cup, the council said in a statement.
It also proposed a €123,000 fine for the Royal Spanish Football Federation as organizer of the Copa del Rey final at Barcelona's Nou Camp ground on May 30th, which Barça won 3-1.
Fans of both sides drowned out the Spanish national anthem with boos and whistles at the start of the match.
The controversy came at a time of high political sensitivities, with Catalan leaders campaigning for independence from Spain ahead of a key regional election expected in September.
The sports council's Antiviolence Commission set various administrative fines for the whistling and for alleged security shortcomings including the burning of flares.
Those targeted by the fines can appeal against them to the state authorities, who will hear their claims before making a final ruling.
The fine against Barcelona consisted of €6,000 for failing to take sufficient action beforehand against groups that called the protests, and €60,000 for security breaches.
The commission issued an €18,000 fine against Athletic Bilbao for failing to crack down on fans who announced their planned protests ahead of the match.
It also issued fines for various Catalan pro-independence civil groups.