Alisson was forced out of Liverpool's 4-1 win over Norwich City on Friday night after going to ground as he prepared to take a goal kick and was replaced by reserve keeper Adrian, who joined Liverpool on a free transfer from West Ham earlier in the week, reports Xinhua news agency.
Speaking after the game Klopp admitted Alisson would not be fit for this week's European Supercup final against Chelsea.
"It's a calf injury," the Reds manager confirmed, saying the keeper "felt as if something hit him from the back. He won't be ready for Wednesday, I can say that already. It is not good but we will find a solution and move on," he added.
Klopp also admitted that despite signing Adrian, Liverpool are short of keepers as their third senior keeper Caoimhin Kelleher works to recover from a broken bone in his hand.
"Caoimhin is back in training but he's not 100 per cent, we have to see what happens," he said.
However Klopp also said he had full confidence in Adrian. "He is a very confident guy. He came in and I don't think he wanted to only sit on the bench for the next couple of years. He made himself ready... you want to have somebody who played the league, who is experienced. He's 32, he's a calm guy, good with his feet. So a lot of good things," he concluded.
( With inputs from IANS )