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In June, a similar shooting attack in the area killed a police officer and wounded two others.
Palestinian National Authority security forces have joined the investigation into the attack, reported the Palestinian news agency Ma'an.
Earlier, the Palestinian Islamic Hamas movement praised the shooting, calling it "an expected response to the crimes of the Israeli occupation," but denied any involvement.
"The armed operation in Hebron emphasizes the presence of the Palestinian resistance in the West Bank" despite Palestinian security programs "that aim at cutting up the resistance," Hamas' military wing Ezz El-Deen Al-Qassam Brigades said in a brief statement.
Israeli responses were divided, with one government minister saying the talks should go on despite the shooting.
"I do not think that we need to give a prize to the murders not to hold talks," Education Minister Gidon Sa'ar said, but added "as we see an Israeli hand extended to peace, we see a murderous response on the part of Palestinians."
Right-wing Knesset member Michael Ben-Ari said the attack was " a reminder to Prime Minister Binyamin Netanyahu who his partners are."
"The Likud government's negotiations with the terrorist Abu Mazen (Abbas) are an energy boost to murderousness and terror. The blood of those harmed is upon the head of the Likud government," The Jerusalem Post newspaper quoted Ben-Ari as saying.