They said the attacker drew a knife on a border police officer at a checkpoint and the officer, who was unharmed, shot her.
She was being taken to hospital in critical condition, and Palestinian sources identified her as Yasmin Al-Zaru, 20.
Israeli police initially said the attacker had been killed before later clarifying her condition.
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 on Saturday.
The latest incident, which followed bloodshed earlier Sunday in Jenin and southeast of Jerusalem, came as US Ambassador to the United Nations Samantha Power visited Israel and the Palestinian territories for talks with leaders from both sides aimed at finding a peaceful resolution to the conflict.
Since the current round of bloodshed erupted at the beginning of October, 170 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.