Enrique has been battling a problem with his right knee in recent weeks and was the subject of arthroscopic surgery to fix the issue.
The 27-year-old, who has not started a match for Liverpool since October 5, will now spend an extended stint on the sidelines.
According to the club's official website, Liverpool expect the Spaniard to return to full training in approximately 10 weeks.
That means Enrique is likely to be missing until February, with Aly Cissokho and John Flanagan filling the left-back role in recent matches.
Liverpool have made a bright start to the Premier League season and sit second, four points adrift of leaders Arsenal.
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