The veteran suffered a torn anterior cruciate ligament in the 3-0 win over Celta Vigo last week, with subsequent tests revealing the extent of the damage.
"The Barca keeper has been operated on by doctors Ulrich Boenisch and Ricard Pruna in Augsburg (Germany) for the anterior cruciate ligament tear he suffered last week," the statement read.
"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."
Valdes had been set to depart the Camp Nou on a free transfer in the summer, but his future is now unclear.