The Liverpool captain was forced off after 10 minutes of their 3-3 draw with Arsenal on Friday.
And the midfielder will be unavailable for the Boxing Day visit of managerless Swansea, who are bottom of the table and four points adrift of safety.
"The problem is that Hendo will not feature for sure, he is out," manager Jurgen Klopp told Liverpool's official website.
"That makes it even worse, the feeling of [the result at Arsenal], because so far we were really okay with this kind of injury and now it happened in the middle of the [busy] period, or whatever.
"[It's] not too cool but I heard nobody else [is injured], a few knocks as it always is, but they should be okay again. That's the situation."