The German, 22, limped off during Thursday's thrilling last-eight victory and left Anfield on crutches.
He is set to miss the rest of the domestic season, including the Reds' semi-final tie against Villarreal.
Fellow midfielder and captain Jordan Henderson will miss the rest of the season with damaged knee ligaments.
Liverpool manager Jurgen Klopp said: "Emre is injured. He will take time. It'll be for the next four or five weeks so we should not say the season is finished."
Should the Reds beat the Spanish side in the last four they will face either Sevilla or Shakhtar Donetsk in the Europa League final on 18 May.
Can joined Liverpool from Bayer Leverkusen for £9.75m in the 2014-15 summer transfer window. This season, the Germany international has played 49 games and scored twice.
Liverpool midfielder Emre Can has been ruled out for at least four weeks after rupturing ankle ligaments in the Europa League win over Borussia Dortmund.