The Spaniard pulled up with the injury and was withdrawn 71 minutes into the Reds’ 3-0 victory at QPR, which was won with a goal from Daniel Agger and a double from Luis Suarez.
Assistant boss Colin Pascoe, who took charge of the team in the absence of Brendan Rodgers who was said to be ill, has now conceded that Liverpool could be without Enrique for some time.
“Unfortunately it looks like he’s got a tear in his hamstring,” he told reporters.
“He was terrific today, absolutely superb, and the way he’s been performing these last couple of months has been a joy to watch.”
“It’s a shame, and hopefully he’s not out for too long.”
The full-back has been one of the most consistent performers at Anfield this season so the news will come as a blow to manager Brendan Rodgers, who has also deployed him in more forward positions in recent weeks.
Liverpool complete their busy round of festive fixtures on Wednesday with a home game against Sunderland, after picking up comprehensive wins over Fulham and QPR, with a defeat away at Stoke sandwiched between.