"(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."
The incident happened 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.
A later statement said the attacker had been taken to a nearby hospital with serious injuries.
Samri said he was 21 years old and from the Hebron area in the south of the occupied West Bank.
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Since October 2015, 242 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.