Having lost Virgil van Dijk for the rest of the season with the knee injured he suffered at Everton, Klopp saw makeshift centre-back Fabinho forced off at Anfield on Tuesday.
Fabinho pulled up with what looked like a hamstring injury in the first half and signalled that he needed to be replaced.
The Brazilian looks certain to miss Saturday’s Premier League game against West Ham and his injury leaves Liverpool desperately short of centre-back options.
Joel Matip is also out injured and Klopp had to turn to 19-year-old Rhys Williams to replace Fabinho against Midtjylland.
Joe Gomez, who has struggled for form this season, is the only fit senior centre-back available to Klopp if Matip is not ready to return against West Ham.
Commentating on the Midtjylland game for BT Sport, Steve McManaman described the injury to Fabinho as “worrying”.