Atletico, who are sixth in the league, secured the last of their nine Cups in 1996 with a 1-0 overtime win over the Catalans, when current Barca boss Pep Guardiola ran their midfield.
Barca trounced Atletico 6-1 at the Nou Camp back in October, but Lionel Messi reckoned that was simply a one-off result.
"They are tough opponents and we know it won't be like the league game," the Argentina forward told the club website (www.fcbarcelona.com).
"We need to remain calm and to continue playing like we have been doing. It's over two legs and we have the return at home."
Barcelona have been in formidable form of late and have won 16 of their last 18 games in all competitions. Atletico have been inconsistent but are unbeaten in 11.
The only remaining non-Primera Liga clubs, Real Union and Poli Ejido both of the Segunda B (third tier), will have home advantage for their first legs against Real Betis and Espanyol respectively.
Poli Ejido knocked out Villarreal 6-1 on aggregate in the last round, and Real Union beat Real Madrid on the away goals rule after drawing 6-6 on aggregate.
Holders Valencia visit Racing Santander, and the 2007 winners Sevilla are at home first to Deportivo Coruna.
A northern derby between Osasuna and 23-times winners Athletic Bilbao, and the clashes between Real Mallorca and Almeria, and Sporting Gijon and Real Valladolid completed the draw.
The first legs are scheduled for Jan. 7, with the return legs on Jan. 14. (Writing by Mark Elkington; Editing by John Mehaffey)
