Germany coach Hansi Flick included Reus in his squad for upcoming international games against Hungary and England,
and was counting on the attacking midfielder as a key member of his World Cup squad.
The World Cup starts in Qatar on November 20. Germany play Japan in Doha three days later, with Spain and Costa Rica also in the group.
The 33-year-old Reus was taken off on a stretcher in the first half of Dortmund's Ruhr derby win against Schalke
on Saturday with what looked like a serious ankle injury.
Reus was in tears after bending his right ankle awkwardly in a challenge for the ball.
"It was a shock for us yesterday when we saw the pictures," Kehl said. "I can give a little good news today
The tests we carried out on Saturday didn't show any break. It's a ligament injury in the ankle."
Reus missed Germany's World Cup win in 2014 with an ankle injury sustained in a warm-up game,
and a groin injury ruled him out of the 2016 European Championship.