The incident occurred at Damascus Gate, a heavily guarded entrance to the Old City and the scene of similar violence in the past.
"Police responded to a life-threatening situation and the female terrorist was shot dead at the scene," police spokesman Micky Rosenfeld said.
Luba Samri, a police spokeswoman, said the 49-year-old woman had "approached a group of officers, pulled out a knife and tried to stab them". She said the woman was a resident of East Jerusalem, which Israel captured along with the West Bank in the 1967 Middle East war.
At least 241 Palestinians have been killed in Israel and the Palestinian Territories in a period of sporadic violence that began in October 2015 but has tapered off in recent months.
Israel says at least 161 were Palestinians who launched stabbing, shooting or ramming attacks using vehicles on Israelis before being killed by Israeli security forces. Others died during clashes and protests.
Two American tourists and 37 Israelis have been killed in such incidents since the violence began.
Israel has accused the Palestinian leadership of inciting the it. The Palestinian Authority, which exercises limited self-rule in the occupied West Bank, denies incitement and charges that in many cases, Israel has used excessive force in thwarting attackers armed with rudimentary weapons.
(Writing by Ori Lewis, Editing by Jeffrey Heller and Mark Trevelyan)
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)