The Wales international picked up the problem in the first half of last weekend’s 2-2 draw with Sunderland at Anfield.
Klopp, who was speaking to the media at Melwood on Friday morning, also revealed that defender Dejan Lovren will also miss this weekend’s trip to Villa Park due to injury.
The Liverpool manager also revealed that Steven Caulker is back available again after a back problem and Martin Skrtel has returned to training following his lay-off with a hamstring injury.
Speaking at a news conference on Friday morning, Klopp said: “Joe unfortunately is out for a while. I think he is a good example: he was in a good way – a really good way – and we tried to manage playing time after his injury when I came here.
“Then he was in good shape, got a little knock on the shoulder, played against Sunderland and I think in the perfect moment of his shape, the muscle stops. Not because of intensity, only because this is how it is.
“In an ideal world you have a long-term pre-season, then play without injuries and nothing will happen. But I think we have to wait a little bit for him, it’s a muscle thing.”
He continued: “[Lovren won’t be fit] for Aston Villa but hopefully for the next game. It’s not a big thing, it’s more about a strange feeling in the muscle.
“It’s the same – he was injured and pushed back. It’s not a real serious thing, but for Aston Villa he has no opportunity.
“Martin Skrtel is back on the pitch outside, but needs his time. Steven had a back problem before the West Ham game. After West Ham he was still in rehab, but yesterday he trained normal so he is available.”
Liverpool head into Sunday’s game looking to return to winning ways after the disappointment of their FA Cup exit at the hands of West Ham United on Tuesday night.
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