The incident took place at a checkpoint outside a flashpoint holy site known to Jews as the Cave of Patriarchs and to Muslims as Ibrahimi Mosque.
A 19-year-old man approached a Border Police officer on duty at a security checkpoint and tried to stab him, according to a statement issued by the Israeli police.
"Officers responded and the suspect was arrested at the scene," the police said, adding that the suspect was not shot.
No injuries were reported at the scene.
The police boosted its forces in the area following the incident.
The incident came amidst tensions in the region following the publication of U.S. President Donald Trump's Middle East peace plan. The Palestinians and most of the Arab world have rejected the plan as biased and unfair.
Israel seized the West Bank in the 1967 Middle East war and has controlled it ever since, despite international criticism.