The former Cameroon international was substituted in the second half of Liverpool’s 4-3 win over Fulham at Anfield on Sunday, and Klopp is concerned about the severity of the problem.
“We lost Joel today”, Klopp said. “No scan yet, but it won't be a short one. We have to get through this.”
Klopp, reflecting on the quality of his side’s goals, said: “I’ve never seen a competitive game with that amount of worldies, beautiful goals. We scored incredible goals. All of them were pretty special.
“But we nearly gave it away. In the first half when we gave the two goals away, the defending was just awful.”
Alexander-Arnold delivered a man-of-the-match performance at Anfield, netting the winner with a volley having also opened the scoring in the first half with a wonderful free-kick which found the net via the crossbar and goalkeeper Bernd Leno’s back.
“Nobody is in doubt how highly I think about Trent”, Klopp said. “His development since I’ve been here is crazy.
"Today he was a real leader on the pitch. That’s probably the biggest improvement [he’s made]. He was just really good.”