One guard was lightly injured in the incident, which occurred near a disputed place of worship in central Hebron, and another border guard killed the assailant, police said in a statement.
According to police, the Palestinian approached a checkpoint close to the site known to Muslims as the Ibrahimi Mosque and to Jews as the Cave of the Patriarchs, where he was asked for identification.
He then drew a knife and attacked one guard, before being chased and shot dead.
Palestinian officials named the youth as 18-year-old Abdallah Ajluni. Earlier police had given his age as 17.
Since October 1, a wave of violence has killed 198 Palestinians, 28 Israelis, two Americans, an Eritrean and a Sudanese, according to an AFP count.
Hebron, the largest city in the West Bank, has long been a source of tensions, with several hundred Israeli settlers living in the heart of the city under heavy military guard among around 200,000 Palestinians.
An AFP journalist said all entrances to the old city were shut down by Israeli soldiers following Saturday's attack.
Many analysts say Palestinian frustration with Israeli occupation and settlement building in the West Bank, the complete lack of progress in peace efforts and their own fractured leadership have fed the unrest.