The Croatia international was forced off after just two minutes of Sunday's 3-1 win over Sevilla and it was initially feared that he had suffered a substantial injury.
However, an MRI scan has revealed a partial tear to his posterior cruciate ligament and a medial collateral ligament sprain, meaning he will not require an operation.
No date has been set for his return, although it is believed he should be able to play again before the end of the season.
A club statement read: "Sime Vrasljko underwent on Monday morning an MRI which revealed a partial tear of his posterior cruciate ligament and a grade I-II sprain in his internal collateral ligament of his left knee.
"The Croatia international defender will begin treatment to recover from his left knee injury."