Both the assailants were shot, with one killed and the other wounded.
There have been almost daily stabbings of Israelis by Palestinians, and an apparent revenge stabbing by an Israeli, in the past fortnight.
Four Israelis and dozens of Palestinians, including attackers, have been killed in the upsurge of violence.
In the latest attack, a woman stabbed the policeman near the headquarters, in the Ammunition Hill area. The wounded policeman managed to shoot and injure the attacker, police said.
Can Israel and the Palestinians contain spiralling violence?
Earlier, an Arab man stabbed a policeman in the Old City after being stopped when he was seen acting suspiciously, police said.
It occurred near the Lions` Gate, scene of several other previous stabbings.
Tensions between Israelis and Palestinians have soared recently, fuelled by clashes at a flashpoint holy site in Jerusalem, in the West Bank, and across the Gaza border, as well as the wave of stabbings.
There were more stabbings at the weekend. Several Palestinians were also killed in clashes with Israeli troops and by an Israeli air strike on a militant site in Gaza in response to rocket fire on Israel.
What is happening between Israelis and Palestinians?
There has been a spate of stabbings of Israelis by Palestinians since early October, and one apparent revenge stabbing by an Israeli. The attacks, in which some Israelis have died, have struck in Jerusalem and elsewhere, and in the occupied West Bank. Israel has tightened security and clashed with rioting Palestinians, leading to deaths on the Palestinian side. The violence has also spread to the border with Gaza.
What`s behind the latest unrest?
After a period of relative quiet, violence between the two communities has spiralled since clashes erupted at a flashpoint Jerusalem holy site in late September. It was fuelled by rumours among Palestinians that Israel was attempting to alter a long-standing religious arrangement governing the site. Israel repeatedly dismissed the rumours as incitement. Soon afterwards, two Israelis were shot dead by Palestinians in the West Bank and the stabbing attacks began. Both Israel and the Palestinian authorities have accused one another of doing nothing to protect each other`s communities.
Is this a new Palestinian intifada, or uprising?
There have been two organised armed uprisings by Palestinians against Israeli occupation, in the 1980s and early 2000s. With peace talks moribund, some observers have questioned whether we are now seeing a third. The stabbing attacks seem to be opportunistic and although they have been praised by militant groups, Palestinian leader Mahmoud Abbas has said Palestinians are not interested in a further escalation.
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