Alba - who has endured an injury-hit campaign - went off 22 minutes into Saturday's match at Camp Nou.
He was replaced by Junior Firpo, who played a key part in teeing up Sergi Roberto's strike - a goal which ultimately proved to be the winner for Barca, who had to hold off a second-half fightback from the visitors.
⚠️ INJURY UPDATE | Tests have confirmed that Jordi Alba has an injured right adductor. He is out and his recovery will determine his availability. pic.twitter.com/jeyltdYUWM— FC Barcelona (@FCBarcelona) February 15, 2020
Barca confirmed during the match that Alba had suffered a problem to his right adductor, with tests subsequently confirming the injury.
It is not yet clear how long the 30-year-old will be sidelined for, but it seems his participation in both the Champions League last-16 tie with Napoli and the Clasico are in doubt.
The victory took Quique Setien's side - temporarily at least - level on points with Madrid at the top of LaLiga, with Zinedine Zidane's side not in action until Sunday.