The Reds have struggled defensively this season due to a succession of problems, prompting the club's hierarchy to bring in QPR's Steven Caulker on loan in the January transfer window.
Since Caulker's arrival, Mamadou Sakho and Dejan Lovren have returned to the fold, while Skrtel had been earmarked for a return to fitness in early February.
Klopp, however, revealed at a press conference on Friday that the Slovakian had aggravated his hamstring and now faces further time on the sidelines.
"We had Skrtel marking Daniel [Sturridge] in training and Martin has re-injured himself," the former Dortmund boss confirmed to the media.
In more positive news for the Anfield side, the manager announced that Jon Flanagan and Joe Allen are closing in on match fitness.
"Jon is back in the race. But it's still early after his injury so we have to be careful," Klopp explained. "[Joe Allen] is close - he got a little knock on his shoulder, we'll see how he is."