According to Marca, only 2,800 of the 13,000 seats at A. Le Coq Arena in Tallinn have been assigned to supporters of the Spanish teams.
The rest of the tickets will be available to the general public, local organising committee, UEFA, national federations, business partners and broadcasters.
Tickets for the Super Cup final will cost between €50 (£43) and €130 (£114).
The match will take place on June 26.