The body of 42-year old Erez Levanon, of Gush Etzion, was found in an alleyway in the Palestinian village of Beit Omar, north of Hebron .
On Monday, the IDF arrested two Palestinians for the murder.
In a statement released on Islamic Jihad's website on Monday evening, the group said two members of its al-Quds Brigades were "able to lure a settler into an agricultural area, and fatally stab him several times."
A spokesman for the Muhammad Sidr Shahid group, part of Islamic Jihad's al-Quds Brigades, was quoted as taking responsibility for the attack by the group's website.
The statement also threatened further "operations against Israeli soldiers and settlers who continue to operate in a criminal manner against the people of Hebron," and added that the murder was "in retaliation for the continued Zionist aggression against the steadfast city of Nablus."
Islamic Jihad's leadership is based in Damascus, Syria, and terror analysts say it is heavily subsidized by Iran.