The Senegal star went off in the first half of the Premier League leaders’ 2-1 victory at Wolves on Thursday.
Mane pulled up when running for a Mohamed Salah pass and was replaced by Takumi Minamino 33 minutes in.
Klopp hopes the injury is not serious but will wait until further checks can be carried out on Friday.
“Sadio, it’s a real shame he had to go off,” he told BBC Sport. “Hopefully, it’s not too bad, just a muscle tweak, but we will see tomorrow.”
Klopp added in a news conference: “He felt something in the hamstring. We don’t know yet; we have to wait.”
Jordan Henderson’s opener was canceled out by Raul Jimenez and Wolves looked to be heading for what would have been a deserved point before Roberto Firmino struck in the 84th minute.
Klopp accepted his side were not at their best, with Wolves’ goal particularly frustrating, but he was delighted with Firmino’s clinical composure.