The 21-year-old has featured in 37 matches across all competitions this season for Hansi Flick's team.
Casado has since pulled out of Spain's Nations League squad due to the injury.
The injury occurred when he was substituted in the 67th minute of Barcelona's dramatic victory over Atletico.
"Tests have confirmed a partial tear of the lateral collateral ligament in his right knee," Barca stated in an official release.
"He will undergo a conservative treatment plan, which is likely to keep him sidelined for about two months."
Currently, Barcelona lead La Liga, sitting level on points with Real Madrid but ahead on goal difference. Atletico Madrid trails them by four points, with Barca also holding a game in hand.
The team is still in the hunt for a potential treble this season.
Barcelona's Copa del Rey semi-final against Atletico is tied 4-4 going into the second leg. Next month, they will meet Borussia Dortmund in the Champions League quarter-finals.