Valdes tore the anterior cruciate ligament in his right knee during Barca's 3-0 win over Celta Vigo on March 26 after landing awkwardly while saving a free-kick.
The 32-year-old Spain international went under the knife in Augsburg, Germany, on Monday morning and Barca confirmed on their website the surgery had gone successfully.
Barca also announced that Valdes would likely be absent for seven months.
"The knee's internal cartilage has been sewn up and the operation was concluded successfully. Valdes will be out of action for approximately seven months."