Manager Brendan Rodgers said the England right back had been suffering with a number of injuries in recent weeks and would spend some time on the sidelines in an effort to get fully fit.
"Glen has played a lot of the season having been injured and really put himself out for the team but unfortunately he's struggled a lot," Rodgers said on the club website (www.liverpoolfc.com).
"The timeline he'll be out will be indefinitely, really. We'll just need to assess that and see how quickly he comes through that.
"He's had a real bad ankle for a period of time and just one or two other issues that haven't allowed him to be 100 percent," said Rodgers.
"I think everyone has seen over many years the speed, fluency and how good he's been but for part of this season he's been restricted and that's obviously been difficult for him.
"But he's put himself out for the team to train and to play and I just think it's now at that point where we need to get him right."
Rodgers also confirmed Brazilian international Lucas Leiva would be out for a "few months" after picking up a knee injury against Aston Villa last weekend.
As the club's only specialist holding midfielder, his absence is a blow to Liverpool's aspirations of a top-four finish and leaves them short on options as they look to maintain their good early season form and qualify for the Champions League for the first time since 2009.
Lucas has been a virtual ever-present this season and his injury could force the club's hand in the January transfer market.
"I am disappointed for Lucas because he's been very, very important for our squad this season. It was something that was innocuous really and has put him out for a few months," Rodgers said.
"Hopefully he'll get back sooner rather than later.
"He'd been in good form this season and had worked his way back into the Brazil squad. Knowing what he is like, he'll be back sooner rather than later - and he'll do everything in his power to get back," said Rodgers.
"In the meantime that leaves us short of a really good player."
Liverpool's squad is being worn increasingly threadbare by a series of injuries particularly in defence where they have lost Mamadou Sakho, Jose Enrique, Jon Flanagan and Daniel Agger recently.
The club, fourth in the Premier League, are yet to make any moves in the transfer market with just nine days of the window remaining.