The attacker "produced a screwdriver and stabbed a policeman in the head, lightly injuring him", police spokeswoman Luba Samri said in a statement.
"Security forces neutralised the terrorist."
She later confirmed he had died of his injuries after being taken to a local hospital.
The assailant struck in the heart of the Old City, a major draw for foreign tourists and pilgrims but the site of several attacks over the past year.
Samri said in a later statement the Palestinian was a 21-year-old and from Beit Surik village near Ramallah in the northern West Bank.
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Since October 2015, 243 Palestinians, 36 Israelis, two Americans, a Jordanian, an Eritrean and a Sudanese have been killed, according to an AFP count.
Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, according to Israeli authorities.
Others were shot dead during protests or clashes, while some died in Israeli air strikes on Gaza.
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