Bender, who needed treatment early in the game and was replaced in the 65th minute, has been diagnosed with a thigh strain which rules him out for a week.
Reus, who left the field in the same minute, picked up a similar injury, but club doctor Markus Braun has forecast a break of two weeks for the Germany international, according to the Westphalian club's website.
Previously, coach Jurgen Klopp said he had "little to complain about" after his side's convincing win.
"This is what we want to see from our team every week, and hopefully we will see it too," he said after his side's second straight win, their biggest since a 6-1 over Stuttgart on November 1.
Henrikh Mkhitaryan scored his first goals since September, earning a reprimand from Klopp in the process.
"He and we know that he's got to show this quality more often," Klopp said. "That was brutally important for him."
The Armenian spoke of his relief after ending his five-month drought.
"Of course I'm very happy because I've scored two goals and we've won," he told reporters. "I'd put myself under too much pressure.
"I think I was able to play more relaxed today and I hope it carries on like this.
"These goals will certainly help relax me even more. To be honest, I had a huge burden weighing me down, but I believed in myself and worked hard, and I hoped things would work out today."
They did for him, but not for Bender or Reus, who have been ruled out of the DFB-Pokal quarter-final against Eintracht Frankfurt on Tuesday and next weekend's Bundesliga clash with the same opponents.
Reus is also a doubt for the first leg of Dortmund's Champions League tie with Zenit St Petersburg on February 25. Klopp is already without Neven Subotic, Ilkay Gundogan and Mats Hummels.