The attack took place near the Old City's Jaffa Gate.
The woman casualty, identified by police spokeswoman Luba Samri as a 25-year-old tourist and a student from England, was stabbed by a 57-year-old Palestinian passenger in the light rail.
A British woman in her twenties has been stabbed to death in Jerusalem according to Israeli media reports, as thousands of Jewish and Christian pilgrims descended on the city's holy sites for Good Friday and the continuing Passover holiday. TV footage showed blood on the floor of the carriage with police officers restraining a man and carrying him away.
Yoram Halevi, a police commander in the city told Israel radio that the suspect had a history of domestic violence and mental illness. It was not immediately possible to resolve the conflicting accounts.
It added that the assailant had previously tried to commit suicide by to swallow a razor blade.
The historic area was packed with Christians celebrating Good Friday and Jews celebrating Passover at the time of the stabbing.
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At least 242 Palestinians have died during the same period.
Apart from Friday's fatality, Palestinians have killed 42 Israelis and two visiting Americans since September 2015, mainly in stabbings, vehicle ramming assaults and shooting attacks.
One of the other youths, 17-year-old Muhammad Mahmoud Ibrahim Al-Hattab, died that day, while the two others, Muhammad Hattab, 18, and Muhammad Moussa Nakhla, 18, were also seriously wounded.
The Palestinian Authority, which exercises limited self-rule in the West Bank, denies incitement and charges that in many cases, Israel has used excessive force in thwarting attackers armed with rudimentary weapons.
Palestinian fears that Israel will seek to change those rules have been the source of repeated violence.