They said the attacker, whose age was not immediately known, drew a knife on a border police officer at a checkpoint and the officer, who was unharmed, shot her dead.
Police spokeswoman Luba Samri said in a statement that the incident took place near the shared religious site known to Jews as the Cave of the Patriarchs and to Muslims as the Ibrahimi Mosque.
The site sees frequent friction between the sides. A 17-year-old Palestinian was shot dead in a stabbing attempt yesterday.
Since the current round of bloodshed erupted at the beginning of October, 171 Palestinians have been killed by Israeli forces. Most were carrying out attacks but others died during clashes and demonstrations.
The violence has claimed the lives of 26 Israelis, as well as an American, a Sudanese and an Eritrean, according to an AFP count.