Left-back Alba attempted to play on after receiving treatment but was forced to make way for Sergi Roberto five minutes before the interval.
Barca did not confirm a timeline for the 30 year-old's return but he will reportedly miss two to three weeks, leaving him set to miss the upcoming LaLiga games against Granada, Villarreal and Getafe.
"Tests carried out have shown that the first-team player Jordi Alba has a hamstring injury in his left leg," the club said via a statement. "The player is now unavailable for action and his recovery will dictate his return."
Alba's injury gives Junior Firpo the chance to push for a first Barca start.
The 23 year-old was signed from Real Betis to provide cover on the left side of defence but has only managed nine minutes in LaLiga this season.
He was left out of the squad that drew 0-0 with Dortmund, a result secured thanks to Marc-Andre ter Stegen's save from Marco Reus's second-half penalty.
Lionel Messi made his return from a calf injury in the Group F encounter, replacing teenager Ansu Fati in the 59th minute.
Barca has five games to play before the next international break, including the Champions League home match against Inter on 2 October.