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 have not confirmed 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 in 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 term.
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' 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 have five games to play before the next international break, including the Champions League home match against Inter on October 2.