The Spaniard has played 28 times for Liverpool in all competitions this season and only recently returned to action after two months out with a hip flexor problem.
Alcantara is set to miss Premier League games against Fulham, Brentford, Leicester City, Aston Villa and Southampton as they push for a top-four finish.
Liverpool are fifth on 56 points, seven behind fourth-placed Manchester United who have a game in hand.