The midfielder was forced off the pitch inside the opening 18 minutes after a coming together with Napoli forward Hirving Lozano.
Speaking after the game, Klopp confirmed Fabinho's injury could be "massive" and it appears his concerns have rung true, with the Brazilian suffering extensive ligament damage to his ankle.
Fabinho underwent scans to reveal the extent of the damage, and it's not good news for him or the Reds, who will be without their star defensive midfielder during the busiest period of the season.
"The midfielder needed to be substituted after 18 minutes of the 1-1 draw at Anfield on Wednesday night after falling awkwardly during a challenge. Further assessment on the injury has discovered Fabinho will be out of action until the New Year.
The Brazilian will begin a rehabilitation programme with the Reds’ medical team at Melwood as he works his way back to full fitness."
Klopp is expected to give his full reaction to the news at his pre-Brighton press conference later on Friday, with the hope that Fabinho can return sooner than in late January/early February.
Games Fabinho Could Miss
Nov 30th: Brighton (H) – 3pm
Dec 4th: Everton (H) – 8.15pm
Dec 7th: Bournemouth (A) – 3pm
Dec 10th: RB Salzburg (A) – 5.55pm
Dec 14th: Watford (H) – 12.30pm
Dec 17th: Aston Villa (A) – 7.45pm
Dec 18th: CWC Semi-Final – 5.30pm
Dec 22nd: CWC Final/Third Place Play-Off – 5.30pm
Dec 26th: Leicester (A) – 8pm
Dec 29th: Wolves (H) – 2pm
Jan 2nd: Sheffield United (H) – 8pm
Jan 11th: Tottenham (A) – 5.30pm
Jan 19th: Man United (H) – 4.30pm
Jan 23rd: Wolves (A) – 8pm