Dortmund won the game 3-1, but the injury to Subotic, who last week put pen to paper on a new contract until 2016, took the gloss off the victory.
"It's not a very pleasant situation for us, but with (Felipe) Santana, we do have somebody who can replace him," the club's general manager Hans-Joachim Watzke said on sport1.de.
Marco Reus was on target for Jurgen Klopp's side in the 3-1 win over Spanish third-division opponents.
"Overall, I'm satisfied," said Klopp. "After the hard training sessions, it was obvious we would not be so sharp."