The 19-year-old was injured during Barcelona's 3-2 extra-time defeat by Athletic Bilbao in the Copa del Rey on 20 January, his second appearance for the club after returning from a two-month spell on the sidelines.
"The first team player Ansu Fati will follow a conservative recovery plan for the injury to the proximal tendon in his left hamstring," Barcelona said in a statement. "His recovery will dictate his return."
Fati has been plagued with injuries since inheriting Barcelona's number 10 jersey from Lionel Messi when the Argentine left for Paris St Germain.
He underwent four surgeries to repair a knee injury sustained in November 2020.