The Spain international, who has struggled with injury this season, suffered a setback in the Copa del Rey defeat and was in tears when he left the field.
Fati has decided against undergoing surgery, with Barcelona revealing that he will follow "a conservative recovery plan".
"The first team player Ansu Fati will follow a conservative recovery plan for the injury to the proximal tendon in his left hamstring. His recovery will dictate his return," read a statement from the Catalan giants.
According to Sport, the 19-year-old will spend the next two to three months on the sidelines recovering from the latest issue.
As a result, the youngster is now expected to be back on the field until at least the end of March, providing that he does not need to undergo an operation at a later date.
Fati, who has scored five goals and registered one assist in 10 appearances for Xavi's side this season, missed the start of the campaign due to his recovery from a knee operation.