The 32-year-old goalkeeper, who has long planned to leave the Nou Camp at the end of his contract in June, fell awkwardly while saving a free-kick in the 22nd minute of Barcelona's 3-0 win over Celta Vigo on Wednesday night.
Valdes could be seen crying as he left the pitch on a cart and Barca later confirmed he had suffered an ACL tear in his right knee, which typically takes at least six months to heal. The injury has ruled the Spain international out of the World Cup and is certain to complicate his search for a new club.
The surgery will take place at the same Augsburg clinic where Real Madrid forward Jese underwent knee ligament reconstruction last week after he suffered an identical injury in a Champions League match with Schalke.
A Barcelona statement confirmed: "According to the club's medical services, Victor Valdes will undergo surgery on his ACL in Augsburg, Germany, on Monday, March 31.
"The surgeons that will conduct the operation are Ulrich Boenisch and Ricard Pruna. After the surgery, FC Barcelona will issue a medical report with the results of the operation."
Meanwhile, Barcelona have agreed a deal to sign sought-after Croatia teenager Alen Halilovic from Dinamo Zagreb.
The 17-year-old attacking midfielder will cost Barca an initial 2.2million euros with add-ons depending on his achievements at the Nou Camp.
Halilovic, who became Croatia's youngest player when he made his international debut against Portugal in a friendly last June, has penned a five-year contract with the Spanish champions and will initially link up with their reserve side.
Halilovic said on fcbarcelona.es: ''I'm delighted and it's difficult to find the words to describe how I feel. Many thanks to Dinamo, who will always remain my first love and the club who made my dreams come true.
''Of course, Barcelona is something special, I've loved the club since I was small and I feel honoured to have the opportunity to play for Barca.
''Before everything, I want to win the double with Dinamo and then focus on my new club.''