Stindl was helped off the pitch in the first half after appearing to severely twist his ankle, and was later taken to hospital for an X-ray.
“I think it’s a torn ligament,” Stindl told broadcaster Sport1 before heading to hospital.
Gladbach sporting director Max Eberl was, however, more optimistic after the X-ray.
“At least he hasn’t broken anything,” he said.
“Lars’ injury was bitter, because he’s a really important player for us,” said teammate Matthias Ginter.
Stindl, 29, has made 11 appearances for world champions Germany since making his debut last June, and was hoping to be included in the squad which national team coach Joachim Loew will announce on May 15.
He now joins Bayern Munich stars Manuel Neuer and Jerome Boateng on a growing injury list for Loew and Germany.
Boateng picked up a groin injury against Real Madrid last Wednesday, while Neuer has missed the last seven months recovering from a fractured metatarsal.
They and Stindl now face a race against time to be fit for Germany’s World Cup opener against Mexico in Moscow on June 17.