Gomez, who moved across to right-back for the game at Turf Moor, was stretchered off in the 23rd minute after a tackle from Ben Mee that saw him crash in to the advertising hoardings.
Whilst Trent Alexander-Arnold replaced the 21-year-old and the Reds went on to win 3-1, the result was marred by Gomez's injury.
Speaking after the game, Klopp confirmed the Englishman was injured and "probably not only a little bit."
Gomez underwent a scan on Thursday and the club have now announced that he suffered a broken left leg that will keep him out of action for six weeks or more.
Klopp's initial fears have been realised, with Gomez missing the entire busy festive schedule, including some crucial games in a season-defining period for the Reds.
Gomez could miss up to nine games for the Reds if he remains out for six weeks. He will miss fixtures against Bournemouth (A), Napoli (H), Man United (H), Wolves (A), Newcastle (H), Arsenal (H), Man City (A), Wolves (A [FA Cup]) and Brighton (A).
His absence will be a huge blow to Liverpool, who have looked accomplished at the back this season with a partnership of Gomez and van Dijk in central defence.
Dejan Lovren will be expected to take his place in the starting eleven, however the Croatian has himself suffered with numerous knocks and has featured just six times this term.
Gomez's absence also affects the Reds at right-back, where he rotates with Alexander-Arnold where needed.
Nathaniel Clyne, who looked set for a move away in January, could be given more chances to feature if Klopp feels he needs to rest Alexander-Arnold.