The Scotland captain sustained the problem on international duty and the club has decided an operation is the best solution.
"There is a little bit there, I think the decision is we go towards surgery," said manager Jurgen Klopp.
"There is a little chance we could try without, but talking to pretty much all experts it looks like surgery will be the best thing, especially in the long term definitely, and that means he is out for a while.
"I don't know exactly how long but it is shoulder surgery so not exactly an easy one.
"In my experience, you can train pretty quickly again but not football-specific because you have to be careful of challenges and all these kinds of things so he will be out for a while."
Liverpool, fourth in the Premier League table, host struggling Everton in the Merseyside derby on Saturday.
