The 28-year-old Spaniard has been struggling with injury all season and has not played since November.
It was initially believed he could be back in action by February after undergoing surgery but his rehabilitation is progressing slowly and manager Brendan Rodgers has admitted the full-back is unlikely to figure in the first team again this season.
"The likelihood is he will miss from now until the end of the season," said the Liverpool boss.
"The priority now is getting him fully fit and getting him ready for next season."
In Enrique's absence, Jon Flanagan has come to the fore, impressing in the back four as the Reds maintained their title challenge.
They are currently top of the league, two points above Chelsea in second and four ahead of third-placed Manchester City, who have two games in hand.