The Spain international was replaced by Adriano after just 15 minutes of the La Liga champions' 3-2 win over Sevilla at Camp Nou on Saturday.
And Barcelona have revealed the defender suffered an issue in his right femoral biceps.
A statement on the club's official website read: "Jordi Alba has undergone medical tests on Sunday morning to determine the exact extent of the injury that occurred during the first half of the match against Sevilla.
"Medical services have confirmed that the player has a broken fibrillar in the femoral biceps of his right leg.
"The recovery time is approximately three weeks."
Alba could now be missing for as many as six Barcelona games.
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