The Belgian striker, on loan from Chelsea, injured his ankle against Schalke on the weekend.
German publication BILD say the 24-year-old has avoided a fracture. But speaking after the loss to Schalke, Stoger said he feared the worst for Batshuayi.
"He is in great pain," Stoger said. "It looked like he could be out for a long time. I hope it's not that bad."
The injury has come at a horrible time for Batshuayi, with his spot in Belgium's World Cup squad under threat if he cannot recover in time.