The Germany international - who was plagued by ankle problems in 2014 - was forced off midway through the second half after a collision with Dennis Erdmann, sparking fears over his fitness.
Ciro Immobile's subsequent brace ensured Dortmund's progression to the last eight, with Reus watching the latter stages from the bench.
And Klopp explained Reus' injury was "only a dead leg".
Dortmund confirmed in a statement on their website that a more detailed diagnosis will be undertaken on Wednesday.
On his side's victory, which sees Dortmund into the quarter-finals of the Pokal for a fourth season running, Klopp added: "It was really difficult.
"The opponent made it difficult for us and the pitch was in a bad condition."
