The goalkeeper is not likely to play competitive football again until October, though whether that will be with the Catalans or elsewhere is still uncertain
The goalkeeper went under the knife on Monday after tearing the anterior cruciate ligament in his right knee early in the 3-0 win over Celta just under a week ago.
"Valdes has been operated on by doctors Ulrich Boenisch and Ricard Pruna in Augsburg for the ACL tear he suffered last week," the club said in a statement on their website.
"The knee’s internal cartilage has been sewn up and the operation was concluded successfully."
Valdes' injury, which rules him out of the World Cup in the summer, has left Gerardo Martino's men with Jose Pinto between the sticks as they enter the crucial point in 2013-14.
The Catalans sit second by a point behind Atletico Madrid in La Liga, will face Diego Simeone's men in the Champions League quarter-final stage - with the first leg at Camp Nou on Tuesday - and have a Copa del Rey final versus Real Madrid to look forward to.
Valdes' intention was to leave Spain upon the expiration of his contract on June 30, with Manchester City and Monaco mooted as potential destinations, though Barca president Josep Maria Bartomeu has claimed he could now stay at the club.