The officer was taken to hospital with "moderate" injuries after the attack in the walled Old City, police spokeswoman Louba Samri said in a statement.
The attacker, brandishing a knife, stabbed the policeman in one of the alleys of the Old City before the wounded officer shot him dead, the statement said.
A wave of unrest that broke out in October 2015 has claimed the lives of 264 Palestinians, 41 Israelis, two Americans, one Jordanian, an Eritrean, a Sudanese and a Briton, according to an AFP count.
Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, the Israeli authorities say.
Others were shot dead during protests or clashes, while some were killed in Israeli air strikes on the Gaza Strip.
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