Due to the impact of the coronavirus pandemic, the 2020-21 tournament will be held in Andalusia, with Malaga, Cordoba and Seville confirmed as the host cities.
Madrid, who won LaLiga last season, will kick-off their campaign in Malaga against 2019-20 Copa del Rey finalists Athletic, the side Los Blancos beat 3-1 on Tuesday.
Barca, qualifying as LaLiga runners-up, were the first name out of the hat in Thursday's draw and will take on Athletic's Basque rivals and Copa del Rey final opponents Real Sociedad in Cordoba.
That tie will be played on January 13, with the second semi-final taking place the following day.
La Real were also Barca's most recent LaLiga opponents on Wednesday, when the Blaugrana claimed a 2-1 win at Camp Nou – labelled their best performance of 2020 by Jordi Alba – to knock the visitors off top spot.
Athletic and La Real are yet to go ahead with last season's Copa final, which was postponed due to COVID-19.
Instead, that game will take place on April 4, two weeks before the 2020-21 final.
Madrid have won the Supercopa on 11 occasions, two fewer than Barca's record haul of 13.
The last of Athletic's two triumphs came in 2015, when they thrashed Barca 5-1 on aggregate over two legs, while La Real's sole title was in 1982.
The 2021 Supercopa final will take place at Seville's Estadio La Cartuja on January 17.