Valdes twisted his knee during a clearance just 20 minutes into the match and had to be carried off the field on a stretcher.
The veteran keeper was taken to a clinic, where doctors determined he had fractured the anterior cruciate ligament in his right knee.
While Barca did not say how long Valdes will be out, he seems likely to miss the remaining eight matches in the La Liga season and may not be available to Spain for the 2014 World Cup, which starts in June.
The win against Celta put Barcelona at the top of La Liga, two points ahead of Real Madrid and Atletico Madrid, though the lead may be short-lived, as both of those clubs were in action Wednesday.
Barca also remains in the chase for the Champions League title, gearing up for a first-leg quarterfinal clash with Atleti next week. Jose Manuel Pinto, 38, replaced Valdes in goal Wednesday and made four creditable saves.
The injury comes at a critical time for both Barca and Valdes, who announced months ago that he planned to leave the club at the end of this season.