Robertson, 29, dislocated his shoulder during Scotland’s 2-0 defeat to Spain last Thursday after colliding with goalkeeper Unai Simon.
The left-back returned to Merseyside earlier this week to undergo scans and was pictured with his right arm in a sling on Wednesday.
And Klopp confirmed the Scotland captain will be sidelined for an extended period. It remains to be seen whether he will return again this calendar year.
"I think the decision will go towards surgery," the manager said.
“A little chance we can try without but all experts say surgery will be the best for the long term and that means he's out for a while. We don't know exactly how long. A shoulder surgery is not an easy one. He will be out for a while."
Greece international Kostas Tsimikas, who has only made one substitute appearance in the league this season, is set to deputise for the foreseeable future.
"Very important to have players like that," [Tsimikas] Klopp added.
"Thank god it's not only Kostas we have like that. Joe Gomez can play that position. We have Luke Chambers and other young boys who show up in training quite frequently. You need options, that's clear. And Kostas is definitely the most experienced in that position. But he can not play all the games from now on, so we need other options."
Cody Gakpo could return to the squad for Saturday's Merseyside derby after taking part in full training on Thursday.
The Dutch forward sustained a knee injury against Tottenham in September and was omitted from the Netherlands squad for their Euro 2024 qualifiers against France and Greece.
Klopp said: "Cody trained once with the team so we will see how it goes for tomorrow. Stefan out, Thiago out. Ben Doak is out, has a little muscle thing. Not available for the weekend. Luke Chambers trains today for the first time after a little ligament issue. Conor Bradley still out."
Prior to the Ukraine clash, the 20-year-old scored a brace in England's 9-1 evisceration of Serbia.
Asked by VAVEL how much he has benefited from the leadership group in the Liverpool squad, Klopp said: "A lot. Since he's here, he grew up, matured, became a man. It was definitely a proud moment for him. You can imagine how proud it made him and his family. If you're a good, young smart footballer you take the right role models in the right moment, the things you see, the things you hear, that's what Harvey is doing.
"You see life how you understand the things happening around you. He's in a really good way, you have to say. Played really well for England, played well for us. There's still space for improvement, he knows that and we are working on that. We are really happy that he came back in with a smile on his face. We asked him if he was still wearing the armband: he wasn't.
"It was a really nice thing [to see]. It means a lot to him."
On Everton, who have won three of their last four games in all competitions, Klopp said: "Everton deserve respect, Calvert-Lewin is back. Real quality. Doucoure, Onana, Gueye, super experienced. Really good centre-halves and England's No.1 in goal. A good team. I understand 'the derby' but I cannot prepare a one-off game, we have to play our best."