The Brazilian, who has this season established himself as a first-choice pick for Jurgen Klopp’s Premier League leaders, was substituted after just 18 minutes of the 1-1 draw at Anfield on Wednesday.
Liverpool have announced that the 26-year-old will play no part in their congested run of 10 games between now and the end of December.
A club statement read: “Liverpool can confirm Fabinho suffered ankle ligament damage during the Champions League encounter with Napoli in midweek.”
“Further assessment on the injury has discovered Fabinho will be out of action until the New Year,” it added.
“The Brazilian will begin a rehabilitation programme with the Reds’ medical team at Melwood as he works his way back to full fitness.”