The injury will see Sissoko miss the remainder of the season.
He told Sky Sports: “I am very, very sad. My form was good, I was consistent enough, scoring goals, and this injury stopped me.
“I am out for the season, however, that is life. Hopefully I will come back stronger next season to help Juve. We have to fight and qualify for the Champions League.
“This season we were unlucky. I don’t think Chelsea were better than us, they took their chances and they had a bit of luck.
“We lost good players such as (Pavel) Nedved in the second game, so it was tough, but Juve will be back soon.”
