The goalkeeper was forced off in the late stages of the first half as Liverpool got their Premier League season under way with a 4-1 victory at Anfield.
And Klopp expects to be without the Brazil international for a period of weeks.
“[It’s] Not too cool. It’s a calf injury which takes him obviously out for a while,” the boss told Liverpoolfc.com.
“I don’t want to make now [an] exact prognosis on when he will be back but it will not be Wednesday for sure, so then we have to see. It takes a while, it takes a couple of weeks for sure, and we have to see.
“I saw already like ‘six weeks’ and stuff like this, but Ali was not a lot injured in his career so I would like to wait a little bit to see how he develops in that process now. But he is not in for the next few weeks.”