Alba, 25, was substituted at half-time of their 2-1 loss at the Estadio de Mestalla on Wednesday, and the club confirmed his right hamstring was the problem area.
"Initial tests confirm that the player sustained an injury to his biceps femoris in his right leg. He will undergo additional tests this Thursday," a statement on the club's website read.
"This isn't the first injury the player has picked up this season.
"In round four, against Sevilla, he picked up a similar injury in the same leg, and when he was practically recovered, he injured his left leg.
"He missed a total of 16 matches."
Alba has been injury prone throughout the season, and scans will reveal whether he can recover for Barca's final five league games this term.
Centre-back Marc Bartra said he felt Barca had the majority of possession in the cup final, but did not capitalise on their midfield dominance.
"Things have not gone our way," he told reporters.
"Possession was ours, but perhaps they have been more effective. They had two real chances and scored twice.
"Now we will go for it in the league."
Barcelona are four points behind Atletico Madrid in the race for the Spanish crown.
