The 21-year-old has made 37 appearances in all competitions this season for Hansi Flick's side.
Casado withdrew from Spain's Nations League squad.
The injury forced him off in the 67th minute of Barcelona's dramatic 4-2 win at Atletico Madrid.
"It has been confirmed that he has a partial tear of the lateral collateral ligament of the right knee," Barcelona said in a statement.
"He will be undergoing conservative treatment that means he is likely to be out of action for two months."
Barcelona are top of LaLiga ahead of Real Madrid on goal difference, with Atletico four points further back, and also have a game in hand.
They are still on course for a possible treble.
Barca's Copa del Rey semi-final against Atletico is level at 4-4 ahead of the second leg. They will face Borussia Dortmund in the Champions League quarter-finals next month.