The 28-year-old suffered the injury just two minutes into Dortmund's 2-2 draw at home to Augsburg on Saturday.
Should the injury be confirmed on Sunday, Poland winger 'Kuba' will be out for the rest of the season.
He would be the second Dortmund star sidelined with a long-term knee injury this season after centre-back Neven Subotic suffered the same fate in November.
"We have only bad news," Klopp said, whose side have picked up just five points in their last seven league games and are 14 points behind Bundesliga leaders Bayern Munich.
"For us this is a disaster, but mainly it's terrible for Kuba (Blaszczykowski). Something like this seems to fit into our season so far, but there has to be a cut-off point (to the injuries) eventually."
Klopp had to patch together a team for most of December as at one point he lost his entire back four to injury.
He still has injured pair centre-back Mats Hummels and midfielder Ilkay Gundogan on the sidelines.