The Brazil international appeared to suffer a knock to his ankle in the 19th minute following a collision with Napoli striker Hirving Lozano.
Fabinho initially attempted to run off the injury before the defensive midfielder was replaced by Georginio Wijnaldum in the Champions League tie.
Liverpool FC can ill-afford to be without their key midfielder given his excellent performances for the Merseyside outfit this term.
The Reds had to come from behind to rescue a point after Liverpool FC centre-half Dejan Lovren netted a 65th-minute header to cancel out Dries Mertens’ first-half goal.
However, Klopp was more concerned about Fabinho’s injury rather than failing to secure a place in the Champions League knockout stage at Anfield on Wednesday night.
“The Fabinho injury is massive,” Klopp told BT Sport. “That’s the biggest thing from tonight. It’s still early and we all hope it’s not too serious but it’s pretty painful in an area you don’t want to have pain.
“We will have to see. That’s our biggest problem right now.”
Liverpool FC are sitting at the top of their group a point ahead of Napoli and three points ahead of Red Bull Salzburg.
The Merseyside outfit will travel to the Austrian club in their final Champions League group-stage fixture on Tuesday 10 December.
Fabinho has scored one goal and has made one assist in 12 games in the Premier League this season.
The Brazilian has featured in 1,006 Premier League minutes so far this season.
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