The attack took place on the light railway close to the Old City, where Christian commemorations were under way for Good Friday.
The attack took place on the light railway close to the Old City, where Christian commemorations were under way for Good Friday as Jews marked the week-long Passover holiday.
The woman, who is her 20s, was in a "critical condition", the emergency services said.
Police had been on high alert for Passover when tens of thousands of Jews pray at the Western Wall inside the Old City and some visit the flashpoint Al-Aqsa mosque compound above it.
The compound, which is the third holiest site in Islam and the holiest site to Jews, who refer to it as the Temple Mount, is the source of constant tensions.
Jews are allowed to visit but not pray at the site.
Palestinian fears that Israel will seek to change those rules have been the source of repeated violence.
A wave of unrest which erupted in October 2015 has claimed the lives of 260 Palestinians, 41 Israelis, two Americans, one Jordanian, an Eritrean and a Sudanese, 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.
The violence has greatly subsided in recent months.