The £97m summer signing from Borussia Dortmund pulled up half an hour into into his first La Liga start at the weekend - a 2-1 win over Getafe in the Spanish capital.
Barca announced on Sunday that the 20-year-old will likely miss the remainder of the year, but there is hope that he will be back up and running for the start of 2018.
A club statement read: "First-team player Ousmane Dembele has been operated on successfully on the rupture to the tendon of the femoral biceps of his left thigh by Dr. Sakari Orava and under the supervision of Dr. Ricard Pruna. The expected period of absence is three and a half months."
Speaking to TVE, club president Josep Maria Bartomeu added: "I have spoken with him, he's affected, but that's normal. He told me he knows everything will be okay, though, and that he's in good hands.
"By Wednesday or Thursday, he will be back in Barcelona. He could return in January, I hope so because that would represent a nice present for all Barcelona fans on Three Kings Day [January 6]."
Dembele has featured just three times for Barcelona since joining in August, totalling 122 minutes in all.