Rivals Barcelona will face newly-promoted Elche, who won the Segunda Division play-off encounter, at Camp Nou, with it still unclear whether Lionel Messi will take part in the contest following his transfer request.
The tie of the round is arguably last season's third-place side, Atletico, taking on Europa League winners Sevilla at the Wanda Metropolitano.
Cadiz will face Osasuna, while Huesca will travel to face highly-fancied Villarreal, who are now coached by Unai Emery.
Matchday One Fixtures
Alaves v Betis
Atletico Madrid v Sevilla
Eibar v Celta
Cadiz v Osasuna
Granada v Atletico
Valencia v Levante
Valladolid v Real Sociedad
Villarreal v Huesca
The first Clasico of the season will be on 25 October 2020 at Camp Nou, while the second is at the Santiago Bernabeu on 11 April 2021.
It was pre-arranged in the draw that the five teams who competed in European competition after the end of the season - Real Madrid, Barcelona, Atletico Madrid, Sevilla and Getafe - along with Segunda Division play-off winners, Elche, would play each other in the first round but have those games have been postponed in round one.
It has also been agreed that despite the tight calendar there will be no games held over Christmas, though the dates of 22 December and 30 December have been approved for fixtures.